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| Orbital Stability of the Sum of $N$ Peakons for the CH-mCH Equation |
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| KeyWord:Camassa-Holm equation, CH-mCH equation, peakons, multi-peakons, orbital stability |
| Author Name | Affiliation | | Dandan He | Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, P. R. China | | Kelei Zhang | Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, P. R. China | | Shengqiang Tang | Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, P. R. China |
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| Abstract: |
| This paper is concerned with a generalization of the modified Camassa-Holm equation with both cubic and quadratic nonlinearities (also known as the CH-mCH equation). We mainly prove the orbital stability of the train of peakons for the CH-mCH equation in energy space, using energy arguments and combining the method of orbital stability of a single peakon with the monotonicity of the local energy norm. |
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