Remarks on solitary waves and Cauchy problem for a Half-wave-Schrödinger equations

2018/10/02 by Yakine Bahri, Bahri, Yakine, Slim Ibrahim +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Spectral Theory in Mathematical Physics #math.AP

paper · pdf · doi:10.48550/arxiv.1810.01385

arxiv created 2018/10/02 · openalex publication_date 2018/10/02 · arxiv updated 2018/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the solitary wave and the Cauchy problem for Half-wave-Schrödinger equations in the plane. First, we show the existence and orbital stability of the ground states. Secondly, we prove that traveling waves exist and converge to zero as the velocity tends to 1. Finally, we solve the Cauchy problem for initial data in L²_xH^s_y(ℝ²), with s>(1)/(2).

Citations

• Orbital stability of standing waves for some nonlinear Schr�dinger equations
• A relation between pointwise convergence of functions and convergence of functionals

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