Some Nonlinear Wave Equations Degenerate Kink Waves

The investigation of the exact solutions of nonlinear evolution equations play important role in the study of nonlinear physical phenomena. For example,the wave phenomema observed in fluid dynamics, plasma and elastic media are often modeled by the bell-shaped sech solutions and the king-shaped tanh solutions.In this article, we study the two types of nonlinear evolution equations:the (3+1) dimensional Breaking Soliton equation and the (3+1dimensional potential-Yu-Toda-Fukuyama equation. By means of the standard Weiss Tabor Carnevale approach and Kruskals simplification, the painleve non-integrability of the (3+1)-dimensional Breaking Soliton equation is easy to be verified.we obtain their bilinear form by choose a different wave transform. some new breathing kink wave solutions,breathing periodic wave solutions and solit-on solutions are obtained by using extended homoclinic test approach and homoclinic test method respectively. some rational breather solutions are obtained by homoclinic breathing limit method.Furthermore, a new nonlinear phenomena, kink degeneracy and periodic degeneracy, are investigated...