On solutions with compact spectrum to nonlinear Klein--Gordon and Schroedinger equations

2021/09/05 by Comech, Andrew
#35B10 #35B40 #35B41 #35Q41 #37K40 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2109.02187

Abstract

We consider finite energy solutions to the nonlinear Schroedinger equation and nonlinear Klein--Gordon equation and find the condition on the nonlinearity so that the standard, one-frequency solitary waves are the only solutions with compact spectrum. We also construct an example of a four-frequency solitary wave solution to the nonlinear Dirac equation in three dimensions.

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