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Symplectic computation of solitary waves for general Sine–Gordon equations

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  • Lu, Xiaowu

Abstract

We present a class of symplectic schemes for the computation of solutions of the general Sine–Gordon systems. These difference methods are constructed based on the symplectic schemes to the infinite-dimensional Hamiltonian system via generating functions. We use these schemes to compute several types of waves phenomena for the Sine–Gordon and the Φ4 systems. It is demonstrated that these schemes preserve the long-time global structure and the topological stabilities of solitary waves very well. Also, our numerical results indicate that these schemes can be used as effective tools for the numerical investigations of the solutions of general Sine–Gordon equations.

Suggested Citation

  • Lu, Xiaowu, 2001. "Symplectic computation of solitary waves for general Sine–Gordon equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 55(4), pages 519-532.
    • Handle: RePEc:eee:matcom:v:55:y:2001:i:4:p:519-532
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    References listed on IDEAS

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    1. Lu, Xiaowu & Schmid, Rudolf, 1997. "A symplectic algorithm for wave equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 43(1), pages 29-38.
    2. Lu, Xiaowu & Schmid, Rudolf, 1999. "Symplectic integration of Sine–Gordon type systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 50(1), pages 255-263.
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