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Numerical study of long-time Camassa–Holm solution behavior for soliton transport

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  • Yu, C.H.
  • Sheu, Tony W.H.

Abstract

In this paper a three-step solution scheme is employed to numerically explore the long-time solution behavior of the Camassa–Holm equation. In the present u−P−α formation, we conduct modified equation analysis to eliminate several leading discretization error terms and perform Fourier analysis for minimizing the wave-like type of error. A three-point seventh-order spatially accurate combined compact upwind scheme is developed for the approximation of first-order derivative term. For the purpose of retaining Hamiltonian and multi-symplectic geometric structures in the non-dissipative Camassa–Holm equation, the adopted time integrator conserves symplecticity. Another main emphasis of this study is to numerically shed light on the scenario of the soliton transport.

Suggested Citation

  • Yu, C.H. & Sheu, Tony W.H., 2016. "Numerical study of long-time Camassa–Holm solution behavior for soliton transport," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 128(C), pages 1-12.
    • Handle: RePEc:eee:matcom:v:128:y:2016:i:c:p:1-12
    DOI: 10.1016/j.matcom.2016.01.008
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