Work

Periodic traveling waves for nonlinear Schrödinger equations with non-zero conditions at infinity in $$ \textbf{R}^2 $$

Year: 2025

Type: article

Abstract: We consider the nonlinear Schrödinger equation with nonzero conditions at infinity in $$\textbf{R}^2$$ R 2 . We investigate the existence of traveling waves that are periodic in the direction transverse to the direction of propagation and minimize the energy when the momentum is kept fixed. We show that for any given value of the momentum, there is a critical value of the period such that traveling waves with period smaller than the critical value are one-dimensional, and those with larger periods depend on two variables.

Source: Calculus of Variations and Partial Differential Equations

DOI: 10.1007/s00526-024-02921-3

Authors: Mihai Mariş, Anthony Mur

Institutions: Université de Toulouse, Institut de Mathématiques de Toulouse

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Institut Universitaire de France, Université Toulouse III - Paul Sabatier, Centre International de Mathématiques et Informatique de Toulouse