Applications of the novel (G′/G) expansion method to find new exact traveling wave solutions of the nonlinear coupled Higgs field equation

Abstract

In this paper, we apply the novel (G'/G)-expansion method to solve nonlinear evolution equations.We investigates the new exact traveling wave solutions of the complex coupled Higgs field equations. This method proved to be very effective in treating nonlinearities as in the case of the prototype considered. Not only does the method provide the general solutions, but also detects special types of exact solutions, such kinks, solitons, cuspon, peakons, periodic waves, and bell type solitary waves. The various waves propagations schemes detected through the novel (G'/G)-expansion method, and their consequent dynamics, are illustrated in graphical representations.