Conservative finite difference schemes for the modified Camassa-Holm equation

Yuto Miyatake, Takayasu Matsuo, Daisuke Furihata
2011 JSIAM Letters  
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.
doi:10.14495/jsiaml.3.37 fatcat:h3ppfpwvdrd7nmpvvi56zno5yu