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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.

MSC:

37L10 Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems
35B10 Periodic solutions to PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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