Solitary waves for Maxwell-Schrodinger equations

TL;DR

This paper investigates the existence, properties, and spectral characteristics of solitary wave solutions in the three-dimensional coupled Schrödinger-Maxwell equations, providing new insights into their mathematical structure.

Contribution

It proves the existence of radial solitary waves with fixed L^2 norm, analyzes their asymptotic behavior and smoothness, and characterizes the eigenvalues as negative and isolated.

Findings

Existence of a sequence of radial solitary waves.

Solutions exhibit specific asymptotic behavior and smoothness.

Eigenvalues are negative and the first is isolated.

Abstract

In this paper we study the solitary waves for the coupled Schr\"odinger - Maxwell equations in three-dimensional space. We prove the existence of a sequence of radial solitary waves for these equations with a fixed $L^2$ norm. We study the asymptotic behavior and the smoothness of these solutions. We show also the fact that the eigenvalues are negative and the first one is isolated.