Smooth Wave Solutions Research Articles

Bifurcations of Travelling Wave Solutions for the B(m,n) Equation

Using the bifurcation theory of dynamical systems to a class of nonlinear fourth order analogue of the B(m,n) equation, the existence of solitary wave solutions, periodic cusp wave solutions, compactons solutions, and uncountably infinite many smooth wave solutions are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact explicit parametric representations of the above waves are determined.

Symmetric and non-symmetric waves in the osmosis K(2, 2) equation

We give an improved qualitative method to solve the osmosis K(2, 2) equation. This method combines several characteristics of other methods. Using this method, the existence of symmetric and non-symmetric wave solutions of the osmosis K(2, 2) equation is studied. Besides abundant symmetric forms such as smooth wave solutions, peaked waves, cusped waves, looped waves, stumpons and fractal-like waves, this equation also admits non-symmetric ones including breaking kink wave solutions, breaking anti-kink wave solutions and rampons. As regards this equation most of those solutions, either symmetric or non-symmetric solutions, have not appeared in the literature. We also study the limiting behavior of all periodic solutions as the parameters tend to some special values.