Nonrelativistic limit of solitary waves for nonlinear Maxwell-Klein-Gordon equations

TL;DR

This paper investigates how solitary wave solutions of nonlinear Maxwell-Klein-Gordon equations transition to solutions of nonlinear Schrödinger-Poisson equations in the nonrelativistic limit, revealing new existence results for lower order nonlinearities.

Contribution

It establishes a connection between solitary waves of NMKG and NSP equations and introduces new existence results for positive solutions with lower order nonlinearities.

Findings

Correspondence between solitary waves of NMKG and NSP in the nonrelativistic limit

Existence of positive solutions to NMKG with lower order nonlinearities

Extension of known solutions to broader parameter ranges

Abstract

We study the nonrelativistic limit of solitary waves from Nonlinear Maxwell-Klein-Gordon equations (NMKG) to Nonlinear Schrodinger-Poisson equations (NSP). It is known that the existence or multiplicity of positive solutions depends on the choices of parameters the equations contain. In this paper, we prove that for a given positive solitary wave of NSP, which is found in Ruiz's work \cite{R}, there corresponds a family of positive solitary waves of NMKG under the nonrelativistic limit. Notably, our results contain a new result of existence of positive solutions to (NMKG) with lower order nonlinearity.