Automodel Solutions of Complex Nonlinear Partial Differential Equation, Possessing Lax Pair

Abstract

The purpose of the study is to find automodel solutions of a complex nonlinear partial differential equation with a Lax pair. The equation under consideration is related to the Dirac scattering operator and is a Schrödinger type equation in terms of the type of linear part, but a nonlinearity type different from it. At the beginning, a system of equations equivalent to the equation under study is considered, its transformation to a form that allows obtaining automodel solutions is demonstrated. Next, an algorithm for finding solutions of this type is applied, as a result, a family of solutions in the form of formal series is obtained.