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Zbl 1181.35222
Zhou, Jiangbo; Tian, Lixin
Solitons, peakons and periodic cusp wave solutions for the Fornberg-Whitham equation. (English)
[J] Nonlinear Anal., Real World Appl. 11, No. 1, 356-363 (2010). ISSN 1468-1218

Summary: We employ the bifurcation method to dynamical systems to investigate the exact travelling wave solutions for the Fornberg-Whitham equation $$u_t - u_{xxt}+u_x+uu_x=uu_{xxx}+3u_xu_{xx}.$$ The implicit expression for solitons is given. The explicit expressions for peakons and periodic cusp wave solutions are also obtained. Further, we show that the limits of soliton solutions and periodic cusp wave solutions are peakons.

MSC 2000:: *35Q51 Solitons
35C07
35C08
35B10 Periodic solutions of PDE
37K50 Bifurcation problems
35B40 Asymptotic behavior of solutions of PDE

Keywords: Fornberg-Whitham equation; soliton; peakon; periodic cusp wave solution

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