带有量子修正的Zakharov方程的精确非线性波解

Exact nonlinear wave solutions for the modified Zakharov equation with a quantum correction

利用动力系统定性理论和分支方法,研究了带有量子修正的Zakharov方程的精确非线性波解,给出了不同参数条件下的相图,沿相图中的特殊轨道进行了积分,得到量子Zakharov方程的4个孤立波解、7个奇异波解和24个周期波解共3类非线性波解。当参数取特殊值时,对部分周期波解取极限,给出了周期波解演化为相应的孤立波解和奇异波解的过程。

The exact nonlinear wave solutions of the Zakharov equation with a quantum correction are investigated by utilizing the bifurcation method and qualitative theory of dynamical systems.The phase portraits under different parameters are given,and we integrate along the special orbits in the phase portraits.Three kinds of nonlinear wave solutions of modified Zakharov equation can be obtained,including 4 solitary wave solutions,7 singular wave solutions and 24 periodic wave solutions.When the parameters H and k take special values,we take the limit of the periodic wave solutions,it is shown that the periodic wave solutions can evolve into corresponding solitary wave solutions and singular wave solutions.