(2+1)维扩展Zakharov-Kuznetsov方程的对称、约化和精确解

The Symmetry Reductions and Exact Solution of the (2+1) Dimensional Extended Zakharov-Kuznetsov Equation

应用经典李群方法得到了扩展Zakharov-Kuznetsov方程的对称和约化方程.通过求解得到的约化方程,结合(G′/G)展开方法、幂级数解法以及Riccati辅助函数法,求出了该方程的一些精确解,包括行波解、有理函数解、幂级数解等.最后,通过对称,进一步求出了该方程的守恒律.

By the application of the classical Lie group method,the symmetry group theorem and reduction equations of the extended Zakharov-Kuznetsov equation.By solving these reduction equations,combined with(G′/G)expansion method,power series expansion method,and Riccati auxiliary function,we find a great many of exact solutions,including traveling wave solutions,rational function solutions,exponential progression solutions and so on.Finally,through the symmetry and adjoint equations,the equation of conservation laws are obtained.