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

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 (J Funct Anal 237(2):655-674, 2006), 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.

Automated summary

In this study, it is shown that there is a correspondence between positive solitary waves of Nonlinear Maxwell-Klein-Gordon equations and Nonlinear Schrodinger-Poisson equations under the nonrelativistic limit. The existence or multiplicity of positive solutions depends on the choices of parameters in the equations. Additionally, a new result of existence of positive solutions with lower order nonlinearity is presented.