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.
['Yu Ch', 'Tony Wen Hann Sheu']
Numerical study of long-time Camassa-Holm solution behavior for soliton transport