an:01679816
Zbl 0985.37072
Li, Jibin; Liu, Zhengrong
Smooth and non-smooth traveling waves in a nonlinearly dispersive equation
EN
Appl. Math. Modelling 25, No. 1, 41-56 (2000).
00070830
2000
j
37K10 35Q58 35B65 76B25 34C37
solitary waves; periodic waves; integrable system; bifurcations of phase portraits; smoothness of waves
Summary: The method of the phase plane is employed to investigate the solitary and periodic traveling waves in a nonlinear dispersive integrable partial differential equation. It is shown that the existence of a singular straight line in the corresponding ordinary differential equation for traveling wave solutions is the reason that smooth solitary wave solutions converge to solitary cusp wave solutions when the parameters are varied. The different parameter conditions for the existence of different kinds of solitary and periodic wave solutions are rigorously determined.