Invariance Analysis of the (2+1) Dimensional Long Dispersive Wave Equation

Journal of Nonlinear Mathematical Physics - Tập 4 - Trang 251-260 - 1997
M. Senthil Velan1, M. Lakshmanan1
1Center for Nonlinear Dynamics, Department of Physics, Bharathidasan University, Tiruchirapalli, India

Tóm tắt

In this paper, we bring out the Lie symmetries and associated similarity reductions of the recently proposed (2+1) dimensional long dispersive wave equation. We point out that the integrable system admits an infinite-dimensional symmetry algebra along with Kac-Moody-Virasoro-type subalgebras. We also bring out certain physically interesting solutions.

Tài liệu tham khảo

Olver P.J., Applications of Lie Groups to Differential Equations, Springer, New York, 1986. Bluman G.W and Kumei S., Symmetries and Differential Equations, Springer, New York, 1989. Lakshmanan M and Kaliappan P., Lie transforms, nonlinear evolution equations and Painlevé forms, J. Math. Phys., 1983, V.24, 795. Ablowitz M.J and Clarkson P.A., Solitons, Nonlinear Evolution Equations and Inverse Scattering Transform, Cambridge University Press, Cambridge, 1990. Konopelchenko B.G., Solitons in Multidimensions, World Scientific, Singapore, 1993. David D., Kamran N., Levi D. and Winternitz P., Symmetry reductions for the Kadomtsev-Petviashvili equation using a loop algebra, J. Math. Phys., 1986, V.27, 1225. Champagne B. and Winternitz P., On the infinite dimensional symmetry groups of the Davey-Stewartson equations, J. Math. Phys., 1988, V.29, 1. Lakshmanan M. and Senthil Velan M., Lie symmetries, infinite dimensional Lie algebras and similarity reductions of certain (2+1) dimensional nonlinear evolution equations, J. Nonlin. Math. Phys., 1996, V.3, 24. Lakshmanan M. and Senthil Velan M., Lie Symmetries, Kac-Moody-Virasoro algebras and integrability of certain higher dimensional nonlinear evolution equations (in preparation) Chakravarthy S., Kent S.L. and Newman E.I., Some reductions of the self-dual Yang-Mills equations to integrable systems in 2+1 dimensions, J. Math. Phys., 1995, V.36, 763. Boiti M., Leon J.J.P. and Pempinelli K., Integrable two-dimensional generalization of the sine-Gordon and sinh-Gordon equations, Inv. Prob., 1987, V.3, 37. Estevez P.G. and Leble S., A wave equation in 2+1: Painlevé analysis and solutions, Inv. Prob., 1995, V.11, 925. Fokas A.S., On the simplest integrable equation in 2+1, Inv. Prob., 1994, V.10, L19. Novikov S., Manakov S.V., Pitaevskii L.P. and Zakharov V.E., Theory of Solitons: The Inverse Scattering Method, Consultants Bureau, New York, 1984. Radha R. and Lakshmanan M., Localized coherent structures and integrability in a generalized (2+1) dimensional nonlinear Schrödinger equation, Chaos, Solitons and Fractals, V.7, 1996 (to appear). Radha R. and Lakshmanan M., Exotic coherent structures in the (2+1) dimensional long dispersive wave equation, J. Math. Phys., 1996, V.37 (to appear). Head A., LIE: a PC program for Lie analysis of differential equations, Comm. Phys. Commun., V.77, 241.