Solution of the Cauchy problem for the Boiti-Leon-Pempinelli equation

The Cauchy problem for the (2+1)-dimensional nonlinear Boiti-Leon-Pempinelli (BLP) equation is studied within the framework of the inverse problem method. Evolution equations generated by the system of BLP equations under study are derived for the resolvent, Jost solutions, and scattering data for the two-dimensional Klein-Gordon differential operator with variable coefficients. Additional conditions on the scattering data that ensure the stability of the solutions to the Cauchy problem are revealed. A recurrence procedure is suggested for constructing the polynomial integrals of motion and the generating function for these integrals in terms of the spectral data.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 2, pp. 163–174, November, 1996.