New solutions of the Schwarzian Korteweg-de Vries equation in 2+1 dimensions based on weak symmetries |
| |
Authors: | M L Gandarias M S Bruzón |
| |
Institution: | (1) Departamento de Matemáticas, Universidad de Cádiz, PO Box 40, 11510 Puerto Real, Cádiz, Spain |
| |
Abstract: | We consider the (2+1)-dimensional integrable Schwarzian Korteweg-de Vries equation. Using weak symmetries, we obtain a system
of partial differential equations in 1+1 dimensions. Further reductions lead to second-order ordinary differential equations
that provide new solutions expressible in terms of known functions. These solutions depend on two arbitrary functions and
one arbitrary solution of the Riemann wave equation and cannot be obtained by classical or nonclassical symmetries. Some of
the obtained solutions of the Schwarzian Korteweg-de Vries equation exhibit a wide variety of qualitative behaviors; traveling
waves and soliton solutions are among the most interesting.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 380–390, June, 2007. |
| |
Keywords: | weak symmetry partial differential equation solitary wave |
本文献已被 SpringerLink 等数据库收录! |
|