BIFURCATION OF SOLITARY WAVES OF THE NONLINEAR EQUATION WITH QUADRATIC POLYNOMIAL POTENTIAL

Abstract

We investigate the bifurcation of solitary waves of the nonlinear wave equation with quadratic polynomial potential u_t + (a+bu+ru^2)u_x+u_xxx=0 with r>0, a, b in R. Use the bifurcation theory of dynamical systems to analyze them qualitatively. Bifurcation parameter sets are shown. Number of solitary waves are given. Explicit solitary wave solutions are obtained.