TY - JOUR
T1 - Smooth and non-smooth travelling waves in a nonlinearly dispersive Boussinesq equation
AU - Shen, Jianwei
AU - Xu, Wei
AU - Lei, Youming
PY - 2005/1
Y1 - 2005/1
N2 - The dynamical behavior and special exact solutions of nonlinear dispersive Boussinesq equation (B(m,n) equation), utt-uxx-a(u n)xx+b(um)xxxx=0, is studied by using bifurcation theory of dynamical system. As a result, all possible phase portraits in the parametric space for the travelling wave system, solitary wave, kink and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions are obtained. It can be shown that the existence of singular straight line in the travelling wave system is the reason why smooth waves converge to cusp waves, finally. When parameter are varied, under different parametric conditions, various sufficient conditions guarantee the existence of the above solutions are given.
AB - The dynamical behavior and special exact solutions of nonlinear dispersive Boussinesq equation (B(m,n) equation), utt-uxx-a(u n)xx+b(um)xxxx=0, is studied by using bifurcation theory of dynamical system. As a result, all possible phase portraits in the parametric space for the travelling wave system, solitary wave, kink and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions are obtained. It can be shown that the existence of singular straight line in the travelling wave system is the reason why smooth waves converge to cusp waves, finally. When parameter are varied, under different parametric conditions, various sufficient conditions guarantee the existence of the above solutions are given.
UR - http://www.scopus.com/inward/record.url?scp=3142705291&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2004.03.034
DO - 10.1016/j.chaos.2004.03.034
M3 - 文章
AN - SCOPUS:3142705291
SN - 0960-0779
VL - 23
SP - 117
EP - 130
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
IS - 1
ER -