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Li, Jibin; Chen, Guanrong

On a class of singular nonlinear traveling wave equations. (English) Zbl 1158.35080

Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 11, 4049-4065 (2007).
A class of singular reaction-diffusion equations is under consideration. The authors study solitons, kink and periodic waves, using methods from the dynamical systems theory. Parametric conditions that guarantee the existence of the the aforementioned solutions are derived and given explicitly.
Reviewer: Igor Andrianov (Köln)

Cited in 12 Reviews
Cited in 142 Documents

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35B10 Periodic solutions to PDEs
35Q51 Soliton equations
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
37K50 Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems

Keywords:

solitary wave; kink wave; periodic wave; breaking wave; bifurcation; nonlinear wave equation; singular reaction-diffusion equation
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References:

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