(3+1)维修正KdV-Zakharov-Kuznetsov方程的行波解  

TRAVELING WAVE SOLUTIONS OF A(3+1)-DIMENSIONAL MODIFIED KDV-ZAKHAROV-KUZNETSOV EQUATION

作　　者：王双特 于恒国 Wang Shuangte;Yu Hengguo(College of Mathematics and Physics,Wenzhou University,Wenzhou 325035,China;Liushi No.3 Middle School,Wenzhou 325604,China)

机构地区：[1]温州大学数理学院,温州325035 [2]乐清市柳市镇第三中学,温州325604

出　　处：《动力学与控制学报》2022年第2期36-44,共9页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(31570364,61871293);国家重点研发计划“政府间国际科技创新合作/港澳台科技创新合作”重点专项资助项目(2018YFE0103700)。

摘　　要：结合动力系统分支理论,对一个非线性(3+1)维修正KdV-Zakharov-Kuznetsov方程进行理论上的研究.首先,根据不同参数值和三次方程判别式分别定性分析了平衡点的类型和相应轨线情况.其次,利用Jacobi椭圆函数,从形式上给出了若干有界行波解和同宿轨的公式,这一结论扩展了已有文献的工作.最后,利用Hamilton函数法数值地给出了几类多模态近似解,以此表明有界行波解的周期性.Combining with bifurcation theory in dynamical systems,a nonlinear(3+1)-dimensional modified KdV-Zakharov-Kuznetsov equation is theoretically investigated.Firstly,based on different parameter values and discriminant in cubic equation,types of equilibria and their corresponding phase portraits are qualitatively analyzed,respectively.Secondly,by the Jacobi elliptical functions,formulas of some bounded traveling wave solutions and homoclinic loops are formally obtained,extending results in literature.Finally,several multi-mode approximations are numerically presented via Hamiltonian method,which indicate periodicity of bounded traveling wave solutions.

关 键 词：(3+1)维修正KdV-Zakharov-Kuznetsov方程 行波解 平衡点 HAMILTON函数 

分 类 号：O415.6[理学—理论物理]