Curriculum Vitae
Nail H. Ibragimov
A
PostScript version of the Curriculum Vitae
- Date and place of birth:
18 January 1939, Russia
- Marital status:
Married Raisa Khamitova in 1980. Two children - Sania (born
26.07.1983, female), Alia (born 25.11.1985, female)
- Present address:
- Department of Computational and Applied Mathematics
University of the Witwatersrand
P.O. Wits 2050, Johannesburg, South Africa
- Telephone (Office): (27)(11)716-3311
Fax: (27)(11)339-7965
E-mail:
nhi@gauss.cam.wits.ac.za
- Degrees:
- M.Sc., Mathematics, 1965, Novosibirsk State University
- Ph.D., Mathematics, 1967, Institute of Mathematics, Novosibirsk
- D.Sc., Mathematics, 1973, Institute of Mathematics, Novosibirsk
- Language proficiency:
- Fluent in English, Russian, Tatar
- Read, understand and can translate into English and Russian
from French, German, Italian
- Read and understand Bashkir, Turkish
- Studied (one year course) Japanese
- Current Position:
- Professor, Department of Computational and Applied
Mathematics, University of the Witwatersrand, South
Africa, July 1994/to date.
- Offices held in International scientific bodies:
- Head of the Research group on Group analysis in
mathematical physics, Institute of Mathematical Modelling,
Russian Academy of Sciences, Moscow, Russia, 1990-1995.
- Supervisor of the Research laboratory of Mathematical
modelling, Ufa Aviation Tech. University, Ufa, Bashkir
Republic, Russia, 1984-1991.
- Previous Appointments:
- Professor, Institute of Mathematical Modelling, Russian
Academy of Sciences, Moscow, May 1990 - September 1993.
- Professor of Mathematics, Faculty of Applied Mathematics
and Computer Science, Moscow State University, January
1988 - June 1993.
- Professor of Mathematics, Department of Mathematics, Moscow
Institute of Physics and Technology, September 1987 -
June 1991.
- Supervisor of the Research laboratory of Mathematical
Modeling, Ufa Aviation Technical University, Ufa, Bashkir
Republic, Russia, January 1984 - September 1991.
- Visiting Professor of Mathematics, Department of Engineering
Sciences, Faculty of Science and Letters, Istanbul
Technical University, Istanbul, Turkey, October 1993 -
July 1994.
- Visiting Professor of Mathematics, Department of
Mathematics, University of Catania, Catania, Italy,
January-February 1991, January-February 1992.
- Visiting Professor of Mathematical Physics, Department of
Physics and Astronomy, University of Georgia, Athens,
Georgia, USA, March-May, 1992.
- Visiting Scientist, Laboratoire de Physique Theorique,
Universite de Pierre et Marie Curie, Paris, June, 1992.
- Visiting Professor of Mathematics, Department of
Mathematics and Applied Mathematics, University of Natal,
Durban, South Africa, November-December, 1992.
- Visiting Professor of Mathematics, Centre de recherches
mathématiques, Université de Montréal,
Montréal, Canada, March-April, 1991.
- Professor of Mathematics, Keldysh Institute of Applied
Mathematics, USSR Academy of Sciences, Moscow, March 1987
to May 1990.
- Director of the Research laboratory of Mathematical
Physics, Bashkir Branch of USSR Academy of Sciences, Ufa,
Bashkir Republic, USSR, 1980-1987.
- Professor of Mathematics, Department of Mathematics, Ufa
Aviation Institute, Ufa, September 1980 to March 1983.
- Head of Department of Applied Mathematics, Ufa Aviation
Institute, Ufa, March 1983 to March 1987.
- Visiting Professor of Mathematics, Department of
Mathematics, University of Greifswald, Greifswald,
Germany, May-June, 1984.
- Professor of Mathematical Physics, Coll\`{e}ge de France,
Paris, Spring, 1980.
- Visiting Scientist, International Center for Theoretical
Physics, Trieste, Italy, July-August, 1980.
- Professor of Applied Mathematics, Faculty of Applied
Mathematics and Mechanics, Novosibirsk State University,
Novosibirsk, September 1967 to June 1980.
- Professor of Mathematics, Institute of Hydrodynamics,
Siberian Branch of USSR Academy of Sciences, Novosibirsk,
June 1969 to November 1980.
- Visiting Professor of Mathematics, Georgia Institute of
Technology, Atlanta, Georgia, USA, October-December, 1976.
- Visiting Professor of Mathematical Physics, Department of
Physics, University of the Pacific, Stockton, California,
USA, January-March, 1977.
- Associate Professor of Applied Mathematics, Faculty of
Applied Mathematics and Mechanics, Novosibirsk State
University, Novosibirsk, September 1967 to September
1973.
- Assistant Professor of Mathematics, Department of
Mathematics, Novosibirsk State University, Novosibirsk,
June 1965 to September 1967.
- Senior Researcher, Institute of Hydrodynamics, Siberian
Branch of USSR Academy of Sciences, Novosibirsk, October
1964 to June 1965.
- Research Fellow, Institute of Hydrodynamics, Siberian
Branch of USSR Academy of Sciences, Novosibirsk, May 1963
to October 1964.
- Research areas:
- Main field - Invariance Principles and Symmetry Analysis
of Mathematical Models of Nature.
- Other fields - Lie Group Analysis of Differential
Equations. Geometry and Relativity. Fluid
Mechanics. History of the Symmetry Analysis in
Mathematics and Physics.
- Current research interests - Theory of Approximate Groups.
Deformations of Symmetry Lie Algebras. Lie-Bäcklund
Transformation Groups. Approximate Representation of the
de Sitter Group and Relativity in the de Sitter
Universe. Invariance Principles in Boundary Value
Problems. Lie Symmetry Analysis of Differential Equation
in Finance.
- Honours, Awards, Membership of Professional Societies:
- Fulbright Scholar, October 1976 - March 1977
- The USSR State Prize in Science and Technics, 1987
- Grant of Russian Fundamental Research (Russian Ac. Sci.),
1992-1993
- NATO Collaborative Research Grant, 1993-1994
- Member of the American Mathematical Society
- Member of the Moscow Mathematical Society
- A-rated researcher by FRD (Foundation for Research
Development, Republic of South Africa) Evaluation, 1995/to
date
- FRD Resarch Grant, 1996
- Membership in Editorial Boards of Journals:
- Differential Equations, 1993/to date
- Dynamics of Continuous Media, 1969-1981
- Lie Groups and Their Applications, Editor, 1994
- Organization of Conferences:
- Co-Chairman of the International Joint IMU/IUTAM Symposium
"Group Theoretic Methods in Mechanics", Novosibirsk, USSR,
1978.
- Chairman of the Annual National conferences in Russia on
``Lie Group Analysis of Differential Equations'', 1983 -
1993.
- Chairman of the Scientific Committee of the International
Workshop ``Modern Group Analysis III'', Ufa, Bashkiria, 1991.
- Chairman of the Scientific Committee of the International
Workshop ``Modern Group Analysis IV: Advanced Analytical
and Computational Methods in Mathematical Physics'',
Catania, Italy, 1992.
- Chairman of the Scientific Committee of the International
Conference ``Modern Group Analysis V: Theory and
Applications in Mathematical Modelling", Johannesburg,
South Africa, 1994.
- Member of the Organizing Committee of the Workshop "Fourth
Workshop on Differential Equations and Chaos",
Johannesburg, South Africa, January 1996.
- Chairman of the Scientific Committee of the International
Conference ``Modern Group Analysis VI: Developments in
Theory, Computation and Applications", Johannesburg, South
Africa, January 1996.
- Invited Lectures:
- Georgia Institute of Technology (Atlanta, USA), 1976-77
- Collège de France (Paris, France), 1979 and 1992
- University of Paris-VI (Paris, France), 1984
- International Center for Theoretical Physics (Trieste,
Italy), 1980
- University of Greifswald (Greifswald, Germany), 1984
- University of Leipzig (Leipzig, Germany), 1984
- University of Catania (Catania, Italy), 1990, 1991 and 1992
- University of Montréal (Montréal, Canada), 1991
- University of Oslo (Oslo, Norway), 1992
- University of Natal (Durban, South Africa), 1993
- University of New South Wales (Sydney, Australia), 1994
- Stanford University (Stanford, USA), 1996
- Lecture series on Modern Group Analysis for
mathematicians of Thailand, Organised by the Ministry of
University Affairs of Thailand (Bangkok, Thailand), 1996
- Number of publications:
- Monographs: 6
- Editor of books: 3
- Editor of conference proceedings: 5
- Chapters in books: 27
- Translations: 3
- Papers: 70
- Papers in preparation: 9
- Communications to scientific meetings: 40
- List of publications:
- MONOGRAPHS:
- Group Properties of Some Differential Equations,
Nauka, Novosibirsk, 1967
- Lie Groups in Some Problems of Mathematical Physics,
Novosibirsk University Press, Novosibirsk, 1972.
- Lie-Bäcklund Transformations in Applications,
SIAM, Philadelphia, 1979 (with R. L. Anderson).
- Transformation Groups Applied to Mathematical
Physics, Nauka, Moscow, 1983 (English translation
by Reidel, Dordrecht, 1985)
- Primer on Group Analysis, Znanie, Moscow, 1989
- Essay on the Group Analysis of Ordinary Differential
Equations, Znanie, Moscow, 1991.
- EDITOR OF BOOKS:
- Handbook of Lie Group Analysis of Differential
Equations. Vol.1: Symmetries, Exact Solutions and
Conservation Laws, CRC Press, Boca Raton, 1994.
- Handbook of Lie Group Analysis of Differential
Equations. Vol.2: Applications in Engineering and
Physical Sciencies, CRC Press, Boca Raton, 1995.
- Handbook of Lie Group Analysis of Differential
Equations. Vol.3: New Trends in Theoretical
Developments and Computational Methods, CRC Press,
Boca Raton, 1996.
- EDITOR OF CONFERENCE PROCEEDINGS:
- Proc. Int. Symp. ``Group Theoretic Methods in
Mechanics'', Novosibirsk, 1978, printed in
Institute of Hydrodynamics, Novosibirsk, 1978 (with
L. V. Ovsyannikov).
- Proc. Int. Workshop ``Modern Group Analysis:
Advanced Analytical and Computational Methods in
Mathematical Physics'', Acireale (Catania), Italy,
October 27-31, 1992, Kluwer Academic Publishers,
Dordrecht, 1993 (with M. Torisi and A. Valenti).
- Proc. Int. Conference ``Modern Group Analysis V:
Theory and Applications in Mathematical
Modelling'', Johannesburg, South Africa, January
16-22, 1994, in: Lie Groups and Their
Applications, vol. 1, No 1, 1994 (with
F. M. Mahomed).
- Proc. Int. Conference ``Modern Group Analysis VI:
Development in Theory, Computation and
Application'', Johannesburg, South Africa, January
15-20, 1996 (in preparation, with F. M. Mahomed).
- ``Differential Equations and Chaos: Lectures on
Selected Topics''. Selected topics presented at
``Fourth Workshop on Differential Equations and
Chaos'', Johannesburg, South Africa, January
12-13, 1996 (in preparation, with F. M. Mahomed,
D. P. Mason and D. Sherwell).
- TRANSLATIONS:
- J. Leray, ``Hyperbolic Differentaial Equations'',
Institute for Advanced Study, Princeton, 1953,
translation from English into Russian and edition,
Nauka, Moscow, 1984.
- J. Leray, ``Garding's Method'', Lecture notes,
translation from French into Russian, Nauka,
Moscow, 1984.
- S. Lie, ``On Integration of a Class of Linear
Partial Differential Equations by Means of Definite
Integrals'', Arch. for Math., Bd. VI, S. 328-368,
translation from German into English, in: CRC
Handbook of Lie Group Analysis of Differential
Equations, vol. 2, CRC Press, Boca Raton, 1995.
- CHAPTERS IN BOOKS:
- Bäcklund transformation for evolution
equations, in Y. Choquet-Bruhat and
C. DeWitt-Morette, Analysis, Manifolds and Physics,
II, North-Holland, 1991.
- One-parameter transformation groups, in
Handbook of Lie Group Analysis of Differential
Equations. Vol.1: Symmetries, Exact Solutions and
Conservations Laws, CRC Press, Boca Raton, 1994.
- Integration of second-order ordinary differential
equations, ibid.
- Group classification of second-order ordinary
differential equations, ibid.
- Invariant solutions, ibid.
- Lie-Bäcklund transformation groups,
ibid, (with R. L. Anderson).
- Noether-type conservation theorems, ibid,
(with R. L. Anderson).
- Ordinary differential equations, ibid.
- Second-order partial differential equations with two
independent variables, ibid, (with
R. K. Gazizov).
- Infinitesimal calculus of symmetry groups, in
Handbook of Lie Group Analysis of Differential
Equations. Vol.2: Applications in Engineering and
Physical Sciencies, CRC Press, Boca Raton, 1995.
- Group classification of differential equations
illustrated by equations of nonlinear filtration,
ibid.
- Invariance principle in linear second-order partial
differential equations, ibid.
- Huygens' principle: conformal invariance, Darboux
transformation, and Coxeter groups, ibid.
- Applications to celestial mechanics and
astrophysics, ibid.
- Utilization of Vessiot-Guldberg-Lie algebra for
integration of nonlinear equation, ibid.
- Symmetry groups and fundamental solutions for linear
equations of mathematical physics, ibid.
- Incompressible fluids, ibid, (with
V. A. Baikov).
- Plasma theory: Vlasov-Maxwell and related equation,
ibid.
- Nonlinear optics and acoustics, ibid.
- Lie-Bäcklund symmetries: representation by
formal power series, in Handbook of Lie Group
Analysis of Differential Equations. Vol.3: New
Trends in Theoretical Developments and
Computational Methods, CRC Press, Boca Raton,
1995}, (with R. L. Anderson).
- Approximate transformation groups and deformations
of symmetry Lie algebras, ibid, (with
V. A. Baikov and R. K. Gazizov).
- Differential equations with distributions: group
theoretic treatment of fundamental solutions,
ibid.
- Calculus of symmetry groups for integro-differential
equations, ibid, (with S. V. Meleshko).
- Group theoretic modelling, ibid.
- Ordinary differential equations, ibid, (with
F. M. Mahomed).
- Differential equations with a small parameter: exact
and approximate symmetries, ibid.
- Differential constraints, ibid, (with
S. V. Meleshko).
- PAPERS:
- Classification of invariant solutions for equations
of two-dimensional
gas motion, Zh. Prikl. Mekh. Tekh. Fiz. 4, 1968
- Transformations preserving harmonic coordinates,
Soviet Math. Dokl. 9,
n.4, 1968
- On the group classification of second order
differential equations,
Soviet Math. Dokl. 9, n.6, 1968
- Invariance of Dirac's equations, Soviet
Math. Dokl. 10, n.2, 1969
- The wave equation in a Riemannian space, Continuum
Dynamics 1,
Novosibirsk, 1969
- Groups of generalized motions, Soviet
Math. Dokl. 10, n.4, 1969
- Invariant variational problems and conservation
laws, Theor. Math.
Phys. 1, n.3, 1969
- Sur le problème de J. Hadamard relatif à
la diffusion des
ondes, C.R. Acad. Sci. Paris, Sér. A, 270,
1970 (with E.V. Mamontov)
- Conformal invariance and Huygens principle, Soviet
Math. Dokl. 11,
n.5, 1970
- The Huygens principle, in: Some Problems of
Mathematics and Mechanics,
Nauka, Leningrad, 1970 (English transl.:
Amer. Math. Soc. Transl. (2) 104,
1976)
- Conservation laws of Hydrodynamics, Soviet Physics
Dokl. 18, 1973
- Conservation laws in Continuum Mechanics,
Proc. Int. Symp. ``Symmetry,
Similarity and Group Theoretic Methods in
Mechanics'', ed. P.G. Glockner and
M.C. Singh, Univ. of Calgary, Calgary, 1974
- Groups of Lie-Bäcklund contact transformations,
Dokl. Akad. Nauk
SSSR, 1975
(with R.L. Anderson)
- Lie-Bäcklund groups and conservation laws,
Soviet Math. Dokl.
17, n.5, 1976
- Applications of Transformations Groups to
Differential Equations,
Lecture notes, Georgia Tech, Atlanta, 1977
- Lie-Bäcklund tangent transformations,
J. Math. Anal. Appl. 59,
n.1, 1977 (with R.L. Anderson)
- On the Cauchy problem for the equation
,
Math. USSR Sbornik 31, n.3, 1977
- Group theoretical nature of conservation theorems,
Lett. Math. Phys. 1,
1977
- Utilization of symmetry groups in computation,
Proc. Int. Symp.
``Group Theoretic Methods in Mechanics'',
Novosibirsk, 1978 (with W.F. Ames)
- Bianchi-Lie, Bäcklund and Lie-Bäcklund
transformations, Proc.
Int. Symp. ``Group Theoretic Methods in
Mechanics'', Novosibirsk, 1978 (with
R.L. Anderson)
- Failure of a correlation between symmetry
properties and Huygens
principle, Proc. Int. Symp. ``Group Theoretic
Methods in Mechanics'',
Novosibirsk, 1978
- The Noether identity, Continuum Dynamics 38,
Novosibirsk, 1979
- On the theory of Lie-Bäcklund transformation
groups, Math. Sbornik
109, n.2, 1979
- Korteweg-de Vries equations from group-theoretic
point of view, Soviet
Phys. Dokl. 24, n.1, 1979 (with A.B. Shabat)
- Lie-Bäcklund algebras of nonlinear
differential equations, Uspekhi
Mat. Nauk 34, n.4, 1979 (with A.V. Zhiber and
A.B. Shabat)
- Equations of Liouville type, Soviet Math. Dokl. 20,
n.6, 1979 (with
A.V. Zhiber and A.B. Shabat)
- Group-theoretic approach to nonlinear evolution
equations, Study Group
on Solitons, Partial Differential Equations and
Spectral Methods, Lecture
Notes, Trieste, 1979
- Evolutions equations with a nontrivial
Lie-Bäcklund group,
Functional Anal. Appl. 14, n.1, 1980 (with A.B. Shabat)
- Infinite Lie-Bäcklund algebras, Functional
Anal. Appl. 14, n.4,
1980 (with A.B. Shabat)
- L-A pairs and infinity of L-B groups and integrals
for nonlinear
evolution equations, Workshop on Nonlinear
Evolution Equations and Dynamical
Systems, Lecture Notes, Chania, Crete, 1980
- Sur l'équivalence des équations
d'évolution, qui admettent
une algèbre de Lie-Bäcklund infinie,
C.R. Acad. Sci. Paris, Sér I,
293, 1981
- Group classifications of filtration equations,
Dokl. Akad. Nauk SSSR,
1987 (with I.Sh. Akhatov and R.K. Gazizov)
- Approximate symmetries of differential equations
with a small parameter,
Preprint, Keldysh Inst. of Appl. Math., 1987 (with
V.A. Baikov and
R.K. Gazizov)
- Bäcklund transformations and nonlocal
symmetries, Soviet Math. Dokl.
36, n.3, 1988 (with I.Sh. Akhatov and
R.K. Gazizov)
- Nonlocal symmetries. Heuristic approach,
Mod. Probl. Math. 34, VINITI,
Moscow, 1989 (with I.Sh. Akhatov and
R.K. Gazizov) (English transl: J. of
Soviet Math. 55, n.1, 1991)
- Nonlocal symmetries of equations of Mathematical
Physics, in: Problems
of Mathematical Physics, Nauka, Moscow, 1989 (with
I.Sh. Akhatov and
R.K. Gazizov)
- Thirteen basic types of gas-dynamics equations, in:
Mathematical
Modeling, Nauka, Moscow, 1989 (with
I.Sh. Akhatov and R.K. Gazizov)
- Approximate group analysis of nonlinear wave
equations, Differential
equations, 1988 (with V.A. Baikov and
R.K. Gazizov)
- Dynamics in the de Sitter Universe: Approximate
representation of the
de Sitter group, Preprint, Keldysh Inst. of
Appl. Math., 1988
- Approximate symmetries, Math. Sbornik 136, n.4,
1988 (with
V.A. Baikov and R.K. Gazizov)
(English transl.: Math. USSR
Sbornik 64, n.2, 1989)
- Approximate groups, Mod. Probl. Math. 34, VINITI,
Moscow, 1989 (with
V.A. Baikov and R.K. Gazizov) (English
transl.: J. of Soviet Math. 55,
n.1, 1991)
- Relationships between the symmetry properties of
the equations of
gas kinetics and hydrodynamics, J. Mathematical
Modeling, vol. 1,
n.3, 1989 (with A.V. Bobylev). (English
transl. in Mathematical
Modeling and Computational Experiment, 1(3),
1993).
- Approximate symmetries and conservation laws,
Proc. V.A. Steklov
Institute of Mathematics, v. 200, Nauka, Moscow, 1991
- Hierarchy of Huygens's equations in spaces with a
nontrivial conformal
group,
Soviet Math. Surveys, 46, n.3, 1991 (with
A.O. Oganesyan)
- Preliminary group classification of equations
,
J. Math. Phys. 32, n.11, 1991 (with
M. Torrisi and A. Valenti)
- Simple method for the group analysis with
applications in Detonation,
J. Math. Phys. 33, n.11, 1992 (with
M. Torrisi)
- Group analysis of ordinary differential equations
and the Invariance
Principle in Mathematical Physics, Soviet
Math. Surveys, vol. 47, n.4,
1992
- Linearization of ordinary differential equations,
in Differential
Equations and Nonlinear Problems of Mathematical
Physics, Academic Press,
New York, 1993
- Group theoretic treatment of fundamental solutions,
Proceedings of the
Conference on
Analysis, Manifolds and Physics, in honour
of
Y. Choquet-Bruhat,
Paris, 1992. Published by Kluwer Academic Press,
Dordrecht, 1994
- Equivalence groups for balance equations,
J. Math. Anal.
Appl., 184(3), 441-452, 1994 (with
M. Torrisi).
- Lie group analysis of differential equations: A
mosaic of results and
open problems, in Proc. of Sophus Lie Memorial
Conference, Oslo,
August 17-21, 1992, Published by Scandinavian
University Press, Oslo, 1994,
O.A.Laudal and B. Jahren, eds.
- Conformal invariance, Huygens principle and
fundamental solutions for
scalar second order hyperbolic equations,
Proceedings of the Int.
Workshop on Modern
Group Analysis: Advanced Analytical and
Computational Methods in Mathematical
Physics, Acireale (Catania), Italy, October
27-31, 1992, Kluwer Academic
Publishers, Dordrecht, 1993 (with
Yu.Yu. Berest and A.O. Oganesyan).
- Sophus Lie and harmony in mathematical physics, on
the 150th
anniversary of his birth, The Mathematical
Intelligencer, vol.16, n.1,
1994
- Approximate Lie algebras and multy-parameter
approximate groups,
Differential equations, vol.29, n.10, 1993
(with V. A. Baikov
and R. K. Gazizov)
- Seven miniatures in group analysis, Differential
equations,
vol.29, n. 10, 1993
- Vessiot-Guldberg-Lie algebra and its application in
solving nonlinear
differential equations, Proc. 11th National
conference Lie group
analysis of differential equations, Samara,
Russia, June 1993.
- Invariants of Lie-Bäcklund transformation
groups generated by
formal power series, Lie Groups and Their
Applications, vol. 1, n. 1,
1994 (with R.L. Anderson)
- Small effects in physics hinted by the Lie group
philosophy: Are they
observable? I. From Galilean principle to heat
diffusion,
Lie Groups and Their Applications, vol. 1,
n. 1, 1994
- Group theoretic determination of fundamental
solutions,
Lie Groups and Their Applications, vol. 1,
n. 2, 1994
(with Yu.Yu. Berest)
- Integration of third-order ordinary differential
equations by Lie's
method: Equations admitting three-dimensional
Lie algebras,
Lie Groups and Their Applications, vol. 1,
n. 2, 1994
(with M.C. Nucci)
- Equivalence transformations of Navier-Stokes
equations,
Bulletin of the Technical University of
Istanbul, vol. 47, n. 1-2,
1994 (with G. Ünal)
- Lie groups in turbulence: Kolmogorov's invariant
and the algebra
,
Lie Groups and Their Applications, vol. 1,
n. 2, 1994
(with G. Ünal)
- Closed orbits and their stable symmetries,
J. Math. Phys.,
vol. 35, n. 12, 1994 (with V.A. Baikov,
R.K. Gazizov, and F.M. Mahomed)
- Approximate equivalence transformations,
Differential Equations,
vol. 30, n. 10, 1994 (with V.A. Baikov and
R.K. Gazizov)
- The problem of invariants for Lie-Bäcklund
groups, in: Modern
Group Theoretical Methods in Physics, Proc. of
the conference in honour of
Guy Rideau, Kluwer Academic Publishers, Dordrecht,
1995, pp. 1-14 (with
R.L. Anderson)
- Semi-scalar representations of the Lorentz group,
and propagation
equations, J. Physics A, vol. 28, 1995,
4083-4087 (with R. Maartens)
- Group analysis of soil water equations, in:
CRC Handbook of Lie Group Analysis of
Differential Equations. Vol.2:
Applications in Engineering and Physical
Sciencies, Ed. N.H. Ibragimov,
CRC Press, Boca Raton, 1995, pp. 228-237 (with
V.A. Baikov, R.K. Gazizov,
and V.F. Kovalev)
- Galilean principle in thermal diffusion,
Symmetri, vol. 2, n. 2,
1995
- Lie symmetry analysis of differential equations in
finance,
Preprint
No. 1/96, University of the Witwatersrand,
Dept. Computational and Applied
Mathematics, Johannesaburg, 1996 (with
R.K. Gazizov)
- Lie symmety analysis of soil water motion equations,
Preprint No. 2/96,
University of the Witwatersrand,
Dept. Computational and Applied
Mathematics, Johannesaburg, 1996 (with
V.A. Baikov,
R.K. Gazizov, and V.F. Kovalev)
- Euler-Lagrange, Lie-Bäcklund and Noether
operators,
Preprint No. 3/96,
University of the Witwatersrand,
Dept. Computational and Applied
Mathematics, Johannesaburg, 1996 (with
A.H. Kara and F.M. Mahomed)
- PAPERS IN PREPARATION:
- Perturbation methods in group analysis
- Lie group analysis of ordinary differential
equations
- Massive galactic halos and dark matter: Unusual
properties of
neutrinos in the De Sitter universe
- Approximate groups: Exponential map
- Invariants of equivalence transformations for
linear third order
ordinary differential equations
- New identities connecting the Euler-Lagrange,
Lie-Bäcklund and
Noether operators (with A. Kara and
F.M. Mahomed)
- Water redistribution in irrigated soil profiles:
Invariant solutions
of the governing equation (with V.A. Baikov,
R.K. Gazizov and V.F. Kovalev)
- Group theoretical touch to the Black-Scholes model
in stock option
pricing: Symmetries, transformations and
fundamental solution
(with R.K. Gazizov)
- Group analysis of differential equations in finance
(with R.K. Gazizov)
Arne Marthinsen <arnema@math.ntnu.no>
Last modified: Mon Nov 25 14:08:04 1996