Bifurcations of travelling wave solutions for the generalization form of the modified KdV equation. (English) Zbl 1045.37045

Summary: By using the theory of bifurcations of dynamical systems to the generalization form of the modified KdV equation, the existence of solitary wave, kink and anti-kink wave solutions and uncountably infinite many smooth and nonsmooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.


37K50 Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
35Q53 KdV equations (Korteweg-de Vries equations)
37J20 Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems
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