论文信息 - Bifurcation of travelling wave solutions in generalized phi-four equation

Bifurcation of travelling wave solutions in generalized phi-four equation

By using the method of planar dynamical systems to a nonlinear variant of the phi-four equation, the existence of smooth and nonsmooth solitary wave (so called peakon and valleyon) and infinite many periodic wave solutions is shown. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of above solutions are given. The formulas to compute the travelling waves are also educed.

Yijun Lou

[1] Brosl Hasslacher,et al. Particle spectrum in model field theories from semiclassical functional integral techniques , 1975 .

[2] Jibin Li,et al. TRAVELING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS , 2002 .

[3] Jibin Li,et al. Smooth and non-smooth traveling waves in a nonlinearly dispersive equation , 2000 .

[4] Peter J. Olver,et al. Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system: II. Complex analytic behavior and convergence to non-analytic solutions , 1997 .

[5] James A. Yorke,et al. Book review: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields , 1985 .

[6] Abdul-Majid Wazwaz,et al. Generalized forms of the phi-four equation with compactons, solitons and periodic solutions , 2005, Math. Comput. Simul..

[7] J. Hale,et al. Methods of Bifurcation Theory , 1996 .

[8] Peter J. Olver,et al. Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system , 1996 .

[9] Farhang Loran. ϕ 4 -model and holography in four dimensions , 2005 .