Symmetries of equations with functional arguments (original) (raw)
Abstract
The method of determination of the Lie symmetry groups of integro-differential equations is generalized to the case of equations with functional arguments. The method leads to significant applications for instance to the nonlocal NLS equation.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.
References (15)
- Z. J. Zawistowski and A. J. Turski: J. Tech. Phys. 39, 115 (1998).
- Z. J. Zawistowski: Bull. Polish Acad. Sci. Tech. Sci. 46, 187 (1998).
- Z. J. Zawistowski: Rep. Math. Phys. 48, No 1/2, 269 (2001).
- Z. J. Zawistowski: Proceedings of Institute of Mathematics of NAS of Ukraine 43, Part 1, 255, (2002).
- L. V. Ovsiannikov: Group Analysis of Differential Equations, Academic Press, Boston 1982.
- P. J. Olver: Applications of Lie Groups to Differential Equations, Springer, New York 1986.
- G. W. Bluman and S. Kumei: Symmetries and Differential Equations, Springer, New York 1989.
- W. I. Fushchych and M. A. Selekhman: Dopovidi Akademii Nauk Ukrainy No 5, 21 (1983) [in Ukrainian].
- W. I. Fushchych, W. M. Shtelen and N. I. Serov: Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics, Kluwer Academic Publishers, Dordrecht 1993.
- N. I. Chetverikov and A. G. Kudryavtsev: Acta Appl. Math., 41, 45 (1995).
- Z. J. Zawistowski and A. J. Turski: J. Tech. Phys. 39, 297 (1998).
- M. Tajiri: J.Phys. Soc. Japan, 52, 1908 (1983).
- W. I. Fushchych and S. S. Moskaliuk: Lett. Nuovo Cimento 31, 571 (1981).
- I. M. Gelfand and S. W. Fomin: Calculus of Variations, Prentice-Hall, Englewood Cliff 1962.
- V. E. Zakharov: Zh. Eksp. Teor. Fiz. 62, 1745 (1972) [in Russian], Sov. Phys. JETP, 35, 908 (1972).