Homoclinic Orbits in Near-Integrable Double Discrete sine-Gordon Equation
نویسنده
چکیده
We establish the existence of homoclinic orbits for the near{integrable double discrete sine-Gordon (dDSG) equation under periodic boundary conditions. The hyperbolic structure and homoclinic orbits are constructed through the B acklund transformation and Lax pair. A geometric perturbation method based on Mel'nikov analysis is used to establish necessary criteria for the persistent of temporally homoclinic orbits for the class of dDSGequations with dissipative perturbations. 1991 MSC 46, 58F07 PACS 02.30Ks, 02.40Vh, 05.45.-a Supported by a TMR postdoctoral fellowship No. ERBFMBICT983236 of Commission of the European Communities, and an EPSRC Grant No. GR/R02702/01.
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