扩展的(G'/G)展开法求量子Zakharov-Kuznetsov方程的精确解  

Using the Improved(G’/G) Expansion Method to Solve the Exact Solutions of the Zakharov-Kuznetsov Equation

作　　者：郭春晓[1] 徐梦桃 郭艳凤[2,3] GUO Chun-xiao;XU Meng-tao;GUO Yan-feng(School of Science,China University of Mining and Technology,Beijing 100083,China;School of Science,Guangxi University of Science and Technology,Liuzhou 545006,China;School of Mathematics and Physics,China University of Geosciences,Wuhan 430074,China)

机构地区：[1]中国矿业大学(北京)理学院,北京100083 [2]广西科技大学理学院,广西柳州545006 [3]中国地质大学(武汉)数理学院,湖北武汉430074

出　　处：《数学的实践与认识》2022年第1期179-187,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11771444,11861013);中国矿业大学(北京)越崎青年学者;广西自然科学基金(2017GXNSFAA198221);中国地质大学(武汉)中央高校科研基金(2018061)。

摘　　要：为得到量子Zakharov-Kuznetsov方程的一些新精确解,借助行波解的思想,结合齐次平衡原理和一类非线性常微分方程解的结构,利用扩展的(G’/G)展开方法,研究了其相应的更加丰富的精确解表达形式.新精确解的表达式主要由双曲函数、三角函数和有理数函数构成,出现了某些怪波解的情形.通过对比不同情况下解的形式,利用Matlab软件给出数值模拟图形,并根据图形的特点分析了一些怪波现象形成的机理.In order to obtain some new exact solutions of quantum Zakharov-Kuznetsov equation,the improved(G’/G) expansion method is applied to study more richer expression of exact solutions with the idea of traveling wave solutions.Here,the homogeneous equilibrium principle has been used and the structure of solutions of a class of nonlinear ordinary differential equations are considered.The new exact solutions are mainly consturctured by hyperbolic functions,trigonometric functions and rational number functions.Some new rogue wave solutions are formed and investigated.The solutions are simulated by Matlab soft on different conditions.Furthermore,the formation mechanism of some rogue wave phenomena is analyzed according to corresponding characters of the figures for the solutions.

关 键 词：量子Zakharov-Kuznetsov方程 扩展的(G’/G)展开法 齐次平衡原理 怪波解 

分 类 号：O175.29[理学—数学]