Traveling Waves for Nonlocal Derivative Nonlinear Schr\"odinger Equations: A Variational Characterization

TL;DR

This paper proves the existence of traveling-wave solutions for a nonlocal derivative nonlinear Schrödinger equation using variational methods, and also establishes nonexistence results via Pohozaev identities.

Contribution

It introduces a variational framework to find traveling-wave solutions for the nonlocal derivative nonlinear Schrödinger equation with general coefficients.

Findings

Existence of minimizers in subcritical and critical cases.

Derivation of Pohozaev-type identities.

Nonexistence results for certain parameter regimes.

Abstract

We establish several existence results for traveling-wave solutions of the nonlocal derivative nonlinear Schr\"odinger equation with general coefficients by variational methods. We study associated minimization problems in the subcritical and critical cases and prove the existence of a minimizer in each case. Finally, we derive Pohozaev-type identities and use them to establish corresponding nonexistence results.