On the solution of the nonlinear Schrödinger equation.
The authors consider the family of Schrödinger equations \[ iq_t+ q_{xx}+ q(| q|^2- S(x,t))= 0.\tag{1} \] In this paper, a complete classification with respect to the function \(S(x,t)\) is given by using the allowed transformation, and the corresponding invariant solution for some special forms of the function \(S(x,t)\) are obtained. The authors also discuss the equation (1) with function \(S(x)\) with allowed transformation and illustrate a technique for constructing wider classes of \(S(x)\) and thus new classes of solutions.
scientific article; zbMATH DE number 2027083