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Periodic nonlinear waves on a half-line

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Abstract

Nontrivial solutions of the equationu tt=u xx−g(u) which are 2π-periodic int and which decay asx → ∞ are shown to exist ifg(a)=0 andg′(0)>1. Breather-like solutions, which also decay asx →–∞, can be interpreted as homoclinic solutions in thex-dynamics; their existence is still in question for generalg.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 94720, Berkeley, California, USA

    Alan Weinstein

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  1. Alan Weinstein
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Communicated by L. Nirenberg

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Weinstein, A. Periodic nonlinear waves on a half-line. Commun.Math. Phys. 99, 385–388 (1985). https://doi.org/10.1007/BF01240354

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  • DOI: https://doi.org/10.1007/BF01240354

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