Second order Lax pairs of nonlinear partial differential equations with Schwarz variants

Details Second order Lax pairs of nonlinear partial differential equations with Schwarz variants Second order Lax pairs of nonlinear partial differential equations with Schwarz variants

2001-08-24

arxiv.org/abs/nlin/0108045v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages, 0 figures, LaTeX form

Scientific paper

In this paper, we study the possible second order Lax operators for all the possible (1+1)-dimensional models with Schwarz variants and some special types of high dimensional models. It is shown that for every (1+1)-dimensional model and some special types of high dimensional models which possess Schwarz variants may have a second order Lax pair. The exiplicit Lax pairs for (1+1)-dimensional Korteweg de Vries equation, Harry Dym equation, Boussinesq equation, Caudry-Dodd-Gibbon-Sawada-Kortera equation, Kaup-Kupershmidt equation, Riccati equation, (2+1)-dimensional breaking soliton equation and a generalized (2+1)-dimensional fifth order equation are given.

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