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Explicit homoclinic tube solutions and chaos for Zakharov system with periodic boundary. (English) Zbl 1187.37112
Summary: In this Letter, the explicit homoclinic tube solutions for Zakharov system with periodic boundary conditions, and even constraints, are exhibited. The results show that there exist two family homoclinic tube solutions depending on parameters $(a,p)$, which asymptotic to a periodic cycle of one dimension. The structures of homoclinic tubes have been investigated.

37L10Normal forms, center manifold theory, bifurcation theory
35B10Periodic solutions of PDE
35Q53KdV-like (Korteweg-de Vries) equations
Full Text: DOI
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