广义Zakharov-Kuznetsov方程的对称及精确解

利用改进的直接方法给出了一类广义Zakharov-Kuznetsov方程ut auux bu2ux cuxxx duxyy=0新显式解与旧显式解之间的关系,并且得到了该方程的对称.这些对称推广了已有文献中应用Steinberg s相似方法获得的结果.利用广义Zakharov-Kuznetsov方程新旧显式解之间的关系,本文在已有显式解的基础上给出了方程新的显式解.这些解对于研究某些复杂的物理现象,以及验证数值求解法则的可行性有重要的意义.

Symmetries and explicit solutions of a generalized Zakharov-Kuznetsov equation

Using an improved direct method,the relationship between new explicit solutions and old ones of a generalized Zakharov-Kuznetsov equation ut auux bu2ux cuxxx duxyy=0 is presented.Applying the relationship to the given solutions in the previous reference,we derive some new explicit solutions of the Zakharov-Kuznetsov equation.These explicit solutions maybe provide a useful help for physicists to study more complicated physical phenomena and for mathematicians to check on the accuracy and reliability of numerical algorithm.The symmetry of the Zakharov-Kuznetsov equation is also presented,which generalizes the results obtained by the Steinberg's similarity method.