Conservation Laws for a Model with both Cubic and Quadratic Nonlinearity

Abstract

In this paper, the conservation laws for a model with both quadratic and cubic nonlinearity$m_t;=;bu_x;+;frac12a;{left[(u^2-u_x^2;m)right]}_x+frac12c;(2m.;u_x+m_x.u);;m=u-u_{xx}$are considered for the six cases of coefficients. By using a variational derivative approach,conservation laws were constructed. The computations to derive multipliers and conservation law fluxes are conducted by using a Maple-based package which is called GeM.