Ansatzes and exact solutions for nonlinear Schrodinger equations

TL;DR

This paper develops ansatzes for three-dimensional nonlinear Schrödinger equations, enabling their reduction to ordinary differential equations, and explores the symmetry properties and relationships among solutions.

Contribution

It provides a comprehensive classification of ansatzes for nonlinear Schrödinger equations and analyzes their symmetry structures and solution relationships.

Findings

Complete description of certain ansatzes

Conditions for reduction to ODEs

Relationship between solutions and symmetries

Abstract

We consider construction of ansatzes for nonlinear Schrodinger equations in three space dimensions and arbitrary nonlinearity, and conditions of their reduction to ordinary differential equations. Complete description of ansatzes of certain types is presented. We also discuss the relationship between solutions, and both Lie and conditional symmetry of these equations.