This article is cited in 3 papers

On a solution of the Cauchy problem for the Boiti–Leon–Pempinelli equation

A. K. Pogrebkov^a, T. I. Garagash<sup>b

a</sup> Steklov Mathematical Institute, Russian Academy of Sciences
^b Landau Institute for Theoretical Physics, Centre for Non-linear Studies

Abstract: Cauchy problem for the $2+1$-dimensional nonlinear Boiti–Leon–Pempinelli (BLP) equation in the framework of the Inverse Problem Method is considered. We derive evolution equations for the resolvent, Jost solutions and Spectral Data of the two-dimensional differential Klein–Gordon operator with variable coefficients that are generated by the considered BLP system of equations. Additional conditions on the Spectral Data that guarantee stability of the solutions of the Cauchy problem, are obtained. We present a recursion procedure for construction of polynomial integrals of motion and generating function of these integrals in terms of Spectral Data.

Received: 14.09.1996

DOI: 10.4213/tmf1219

 English version: Theoretical and Mathematical Physics, 1996, 109:2, 1369–1378

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