Stability of peakons for the Degasperis‐Procesi equation |
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| Authors: | Zhiwu Lin Yue Liu |
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| Institution: | 1. University of Missouri‐Columbia, Department of Mathematics, Columbia, MO 65211;2. University of Texas at Arlington, Department of Mathematics, Arlington TX 76019 |
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| Abstract: | The Degasperis‐Procesi equation can be derived as a member of a one‐parameter family of asymptotic shallow‐water approximations to the Euler equations with the same asymptotic accuracy as that of the Camassa‐Holm equation. In this paper, we study the orbital stability problem of the peaked solitons to the Degasperis‐Procesi equation on the line. By constructing a Lyapunov function, we prove that the shapes of these peakon solitons are stable under small perturbations. © 2007 Wiley Periodicals, Inc. |
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