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Stability of Peakons for an Integrable Modified Camassa-Holm Equation with Cubic Nonlinearity |
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| Authors: | Changzheng Qu Xiaochuan Liu Yue Liu |
| Institution: | 1. Department of Mathematics, Ningbo University, Ningbo, 315211, P. R. China 2. Department of Mathematics, Northwest University, Xi’an, 710069, P. R. China 3. Department of Mathematics, University of Texas, Arlington, TX, 76019-0408, USA |
| Abstract: | Considered herein is the dynamical stability of the single peaked soliton and periodic peaked soliton for an integrable modified Camassa-Holm equation with cubic nonlinearity. The equation is known to admit a single peaked soliton and multi-peakon solutions, and is shown here to possess a periodic peaked soliton. By constructing certain Lyapunov functionals, it is demonstrated that the shapes of these waves are stable under small perturbations in the energy space. |
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