Traveling Waves for Nonlocal Derivative Nonlinear Schrödinger Equations: A Variational Characterization

2026/03/31 by Amin Esfahani, Adilbek Kairzhan, Mukhtar Karazym
Mathematics · #math.AP

paper · pdf

Abstract

We establish several existence results for traveling-wave solutions of the nonlocal derivative nonlinear Schrödinger 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.

Citations

• On the well-posedness of the intermediate nonlinear Schrödinger equation on the line
• Traveling periodic waves and breathers in the nonlocal derivative NLS equation
• On the orbital stability of solitary waves for the fourth order nonlinear Schrödinger equation
• The Calogero--Moser Derivative Nonlinear Schrödinger Equation
• Existence and decay of traveling waves for the nonlocal Gross-Pitaevskii equation
• Getting acquainted with the fractional Laplacian
• On the stability of the solitary waves to the (generalized) kawahara equation
• Note on a modification to the nonlinear Schrödinger equation for application to deep water waves

Related

• Traveling Waves of Discrete Nonlinear Schrodinger Equations with Nonlocal Interactions
• Variational problems for the system of nonlinear Schrödinger equations with derivative nonlinearities
• Traveling periodic waves and breathers in the nonlocal derivative NLS equation
• Solitary waves in nonlocal NLS with dispersion averaged saturated nonlinearities
• Traveling waves for nonlinear Schrödinger equations