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Communications in Mathematical Physics

, Volume 158, Issue 2, pp 397–430 | Cite as

Nonpersistence of breather families for the perturbed sine Gordon equation

  • Jochen Denzler
Article

Abstract

We show that, up to one exception and as a consequence of first order perturbation theory only, it is impossible that a large portion of the well-known family of breather solutions to the sine Gordon equation could persist under any nontrivial perturbation of the form
$$u_{tt} - u_{xx} + \sin u = \varepsilon \Delta \left( u \right) + O\left( {\varepsilon ^2 } \right),$$
where δ is an analytic function in anarbitrarily small neighbourhood ofu=0. Improving known results, we analyze and overcome the particular difficulties that arise when one allows the domain of analyticity of δ to be small. The single exception is a one-dimensional linear space of perturbation functions under which the full family of breathers does persist up to first order in ε.

Keywords

Neural Network Statistical Physic Complex System Analytic Function Sine 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Jochen Denzler
    • 1
  1. 1.Mathematisches InstitutLudwig-Maximilians-UniversitätMünchenGermany

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