广义Zakharov-Kuznetsov方程的对称及精确解(英文)  

Symmetries and explicit solutions of a generalized Zakharov-Kuznetsov equation

作　　者：闫志莲[1] 刘希强[2] 

机构地区：[1]安徽工业大学数理学院,马鞍山243002 [2]聊城大学数学科学学院,聊城252059

出　　处：《原子与分子物理学报》2007年第1期141-144,共4页Journal of Atomic and Molecular Physics

基　　金：山东省自然科学基金(2004ZX16)

摘　　要：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.Using an improved direct method,the relationship between new explicit solutions and old ones of a generalized Zakharov-Kuznetsov equation ut＋auux＋bu^2ux＋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.

关 键 词：广义Zakharov-Kuznetsov方程 对称 显式解 精确解 

分 类 号：O175.29[理学—数学] O241.82[理学—基础数学]