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

Sen-yue Lou·Xiao-yan Tang·Qing-Ping Liu·T. Fukuyama
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Abstract

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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Sen-yue Lou, Xiao-yan Tang, Qing-Ping Liu, T. Fukuyama. 2001-09-14. Second order Lax pairs of nonlinear partial differential equations with Schwarz variants. https://arxiv.org/abs/nlin/0108045

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