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

C.H. Yu and Tony W.H. Sheu

Mathematics and Computers in Simulation (MATCOM), 2016, vol. 128, issue C, 1-12

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.

Keywords: Camassa–Holm equation; Seventh-order spatially accurate; Symplecticity (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:128:y:2016:i:c:p:1-12

DOI: 10.1016/j.matcom.2016.01.008

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