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Extension on peakons and periodic cusp waves for the generalization of the Camassa–Holm equation
Author(s) -
Wen Zhenshu
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3226
Subject(s) - cusp (singularity) , phase portrait , generalization , mathematics , bifurcation , camassa–holm equation , extension (predicate logic) , mathematical analysis , nonlinear system , qualitative analysis , bifurcation theory , physics , geometry , computer science , qualitative research , integrable system , social science , quantum mechanics , sociology , programming language
In this paper, we employed the bifurcation method and qualitative theory of dynamical systems to study the peakons and periodic cusp waves of the generalization of the Camassa‐Holm equation, which may be viewed as an extension of peaked waves of the same equation. Through the bifurcation phase portraits of traveling wave system, we obtained the explicit peakons and periodic cusp wave solutions. Further, we exploited the numerical simulation to confirmthe qualitative analysis, and indeed, the simulation results are in accord with the qualitative analysis. Compared with the previous works, several new nonlinear wave solutions are obtained. Copyright © 2014 John Wiley & Sons, Ltd.