Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4615595 | Journal of Mathematical Analysis and Applications | 2015 | 16 Pages |
Abstract
Traveling wave solutions to a class of dispersive models,utâutxx+uux=θuuxxx+(1âθ)uxuxx, are investigated in terms of the parameter θ, including two integrable equations, the Camassa-Holm equation, θ=1/3, and the Degasperis-Procesi equation, θ=1/4, as special models. It was proved in H. Liu and Z. Yin (2011) [39] that when 1/2<θâ¤1 smooth solutions persist for all time, and when 0â¤Î¸â¤12, strong solutions of the θ-equation may blow up in finite time, yielding rich traveling wave patterns. This work therefore restricts to only the range θâ[0,1/2]. It is shown that when θ=0, only periodic travel wave is permissible, and when θ=1/2 traveling waves may be solitary, periodic or kink-like waves. For 0<θ<1/2, traveling waves such as periodic, solitary, peakon, peaked periodic, cusped periodic, or cusped soliton are all permissible.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Tae Gab Ha, Hailiang Liu,