Variational statement of the Schrödinger equation with a nonstationary nonlinearity and its integrals of motion
The authors consider a system of equations which model the propagation of super short laser radiation in a nonlinear medium. This system includes a nonlinear and nonlocal Schrödinger equation with cubic nonlinearity. The system under consideration is not Lagrangian. A variational formulation of the problem is posed, and an inverse variational problem is solved by using integrating factors. Generalized conservation laws are also obtained.
scientific article; zbMATH DE number 7043436