A. I. Zenchuk, “Some generalizations of the 2-dimensional Toda chain and <nobr>$\operatorname{sh}$</nobr>-Gordon equation”, TMF, 1997, Volume 110, Number 2,Pages <nobr>233

This article is cited in 7 papers

Some generalizations of the 2-dimensional Toda chain and $\operatorname{sh}$-Gordon equation

A. I. Zenchuk

L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Abstract: We study the discrete transformations of the solutions and potentials of the second order partial differential equation with two independent variables. These transformations are introduced by the formula $D=V_1\partial_x+V_2\partial_y+V_3$. The simplest closed chains of these transformations are considered. The integrability of the derived nonlinear equations by the IST-method is proved.

Received: 19.06.1996

DOI: 10.4213/tmf964