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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2017, Vol. 32 Issue (1): 33-40    DOI:
    
The new complexion solutions of the (2+1) dimension modified Zakharov-Kuznetsov equation 
Taogetusang
The College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China
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Abstract   The method combing the function transformation, the variables separation type solutions and the first kind of elliptic equation is presented to construct many kinds of new complexion solutions of the (2+1) dimension modified Zakharov-Kuznetsov equation. Step1, two kinds of function transformations are presented, and the (2+1) dimension mZK equation can be changed to the nonlinear evolution equation that can obtain the variables separation type solutions. Step2, the variables separation type solutions of the nonlinear evolution equation are presented, and by the relative conclusions of the first kind of elliptic equation, the two-soliton solutions and the two-period solutions and other new complexion solutions of the (2+1) dimension mZK equation are constructed.

Key words： function transformation      the (2+1) dimension mZK equation      the first kind of elliptic equation      the new complexion solutions     
Received: 08 April 2016      Published: 18 March 2018
CLC:  O175.14  
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Taogetusang. The new complexion solutions of the (2+1) dimension modified Zakharov-Kuznetsov equation . Applied Mathematics A Journal of Chinese Universities, 2017, 32(1): 33-40.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2017/V32/I1/33


(2+1)维modified Zakharov-Kuznetsov方程的复合型新解

给出函数变换, 变量分离形式解与第一种椭圆方程相结合的方法, 构造了(2+1)维modified Zakharov-Kuznetsov(mZK)方程的多种复合型新解. 步骤一, 给出两种函数变换, 将(2+1)维mZK方程转化为能够获得变量分离解的非线性发展方程.步骤二, 给出非线性发展方程的变量分离形式解, 通过第一种椭圆方程及其相关结论,构造了(2+1)维mZK方程的双孤子解和双周期解等复合型新解.

关键词： 函数变换,  (2+1)维mZK方程,  第一种椭圆方程,  复合型新解 
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