Conservative finite difference schemes for the modified Camassa-Holm equation
Conservative finite difference schemes for the modified Camassa-Holm equation
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DOI：
10.14495/jsiaml.3.37
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Y. Miyatake;Takayasu Matsuo;Daisuke Furihata
中科院分区：
文献类型：
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作者：
Y. Miyatake;Takayasu Matsuo;Daisuke Furihata
我们考虑修正Camassa-Holm方程的数值积分，该方程最近由McLachlan和Zhang（2009）提出，作为著名Camassa-Holm方程的推广。给出了同时保持两个不变量的修正方程的非线性和线性有限差分格式。我们还给出了所提出方案的一些数值例子，其中发现mCH的某些解可以表现得像孤子。
We consider the numerical integration of the modified Camassa-Holm equation, which has been recently proposed by McLachlan and Zhang (2009) as a generalization of the prominent Camassa-Holm equation. We present nonlinear and linear finite difference schemes for the modified equation that preserve two invariants at a same time. We also show some numerical examples of the presented schemes, where it is found that certain solutions of the mCH can behave like solitons.