A non-local approach to waves of maximal height for the Degasperis-Procesi equation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:479

Article

关键词: Degasperis-Procesi;    Global bifurcation;    Peaked waves;   

DOI  :  10.1016/j.jmaa.2019.06.014

来源: Elsevier

【 摘 要 】

We consider the non-local formulation of the Degasperis-Procesi equation u(t) + uu(x) + L(3/2u(2))(x) = 0, where L is the non-local Fourier multiplier operator with symbol m(xi) = (1 + xi(2))(-1). We show that all L-infinity, pointwise travelling-wave solutions are bounded above by the wave-speed and that if the maximal height is achieved they are peaked at those points, otherwise they are smooth. For sufficiently small periods we find the highest, peaked, travelling-wave solution as the limiting case at the end of the main bifurcation curve of P-periodic solutions. The results imply that there are no L-infinity travelling cuspon solutions to the Degasperis-Procesi equation. (C) 2019 The Author. Published by Elsevier Inc.

【 授权许可】

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