Conservation Laws for a Model with both Cubic and Quadratic Nonlinearity

Authors : Hatice TAŞKESEN, Mohanad ALALOUSH

Pages : 180-185

View : 19 | Download : 10

Publication Date : 2019-12-20

Article Type : Research Paper

Abstract :In this paper, the conservation laws for a model with both quadratic and cubic nonlinearity  \begin{eqnarray*} m_{t}=bu_{x}+\frac{1}{2}a\left[ \leftinsert ignore into journalissuearticles values( u^{2}-u_{x}^{2}\right); m\right] _{x}+% \frac{1}{2}c\leftinsert ignore into journalissuearticles values( 2m\cdot u_{x}+m_{x}\cdot u\right); ;\text{ \ \ }m=u-u_{xx} \end{eqnarray*}% 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.
Keywords : Conservation laws, Integrable equations, Multiplier