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.