Some properties of nonlinear generalization of Schrödinger equation

Abstract

Author presents a nonlinear generalization of Schrödinger equation, allowing exact analytical solutions. He shows that in the case of the dynamic Schrödinger equation there exist a simplest nonlinear generalization whose exact soliton-types solutions are related with solutions of the stationary Schrödinger equation. For the latter case, a nonlinear generalization with qualitatively yhe same, althought compressed or extended (depending on the value of the nonlinearity parameter) spectrum of a corresponding linear Schrödinger equation is proposed. [...].