Solutions with compact time spectrum to nonlinear Klein--Gordon and Schroedinger equations and the Titchmarsh theorem for partial convolution

Abstract

We prove that finite energy solutions to the nonlinear Schroedinger equation and nonlinear Klein--Gordon equation which have the compact time spectrum have to be one-frequency solitary waves. The argument is based on the generalization of the Titchmarsh convolution theorem to partial convolutions.

15 pages

References in corpus (3)

• Breathers in PT-symmetric optical couplers
• Global attractor for a nonlinear oscillator coupled to the Klein-Gordon field
• Spectral stability of bi-frequency solitary waves in Soler and Dirac--Klein--Gordon models

Cited by in corpus (1)

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