By using the bifurcation theory of planar dynamical systems to a class of nonlinear evolution equations, the existence of traveling wave solutions is showed. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Explicit exact parametric representations of some traveling wave solutions are obtained.

Abstract A multiple exp-function method for exact multiple wave solutions of nonlinear partial differential equations is proposed. The method is oriented towards the ease of use and capability of computer algebra systems and provides a direct and systematic solution procedure that generalizes Hirota’s perturbation scheme. With the help of Maple, applying the approach to the (3 + 1)-dimensional ...

By using the bifurcation theory of dynamical systems, we study the coupled Higgs field equation and the existence of new solitary wave solutions, and uncountably infinite many periodic wave solutions are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. All exact explicit parametric representations of the ...

We present a method for generating exact diagonal G2-cosmological solutions in dilaton gravity coupled to a radiation perfect fluid and with a cosmological potential of a special type. The method is based on the symmetry group of the system of G2-field equations. Several new classes of explicit exact inhomogeneous perfect fluid scalar-tensor cosmologies are presented.