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Cai, Huixian; Pan, Chaohong; Liu, Zhengrong

Some interesting bifurcations of nonlinear waves for the generalized Drinfel’d-Sokolov system. (English) Zbl 1470.35305

Abstr. Appl. Anal. 2014, Article ID 189486, 20 p. (2014).
Summary: We study the bifurcations of nonlinear waves for the generalized Drinfel’d-Sokolov system \(u_t +(v^m)_x = 0, v_t + a(v^n)_{x x x} + b u_x v + c u v_x = 0\) called \(D(m, n)\) system. We reveal some interesting bifurcation phenomena as follows. (1) For \(D(2, 1)\) system, the fractional solitary waves can be bifurcated from the trigonometric periodic waves and the elliptic periodic waves, and the kink waves can be bifurcated from the solitary waves and the singular waves. (2) For \(D(1, 2)\) system, the compactons can be bifurcated from the solitary waves, and the peakons can be bifurcated from the solitary waves and the singular cusp waves. (3) For \(D(2, 2)\) system, the solitary waves can be bifurcated from the smooth periodic waves and the singular periodic waves.

Cited in 2 Documents

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35B32 Bifurcations in context of PDEs
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