Abstract
The dynamical behavior and special exact solutions of nonlinear dispersive Boussinesq equation ( B ( m , n ) equation), u tt − u xx − a ( u n ) xx + b ( u m ) 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.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
