Periodic cusp wave solutions and single-solitons for the b-equation

Boling Guo and Zhengrong Liu

Chaos, Solitons & Fractals, 2005, vol. 23, issue 4, 1451-1463

Abstract: In this paper, we employ the bifurcation method of dynamical systems and the numerical simulation approach of differential equations to study periodic cusp wave solutions and single-solitons for the b-equationut-uxxt+(b+1)uux=buxuxx+uuxxxwith b>1. The explicit representations of periodic cusp waves and the implicit expressions of single-solitons are obtained. Further, we show that the limits of both periodic cusp waves and single-solitons are peakons which possess explicit expression u=ce−∣x−ct∣. As corollary, the single-solitons equations of the Camassa–Holm equation and the Degasperis–Procesi equation are given. Our theoretical derivations are identical with the numerical simulations.

Date: 2005
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:23:y:2005:i:4:p:1451-1463

DOI: 10.1016/j.chaos.2004.06.062

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