一类广义时空分数阶耦合Zakharov方程组新的解析解  

New analytic solutions for a class of generalized time-space fractional coupled Zakharov equations

作　　者：洪宝剑[1] 朱永康 瞿新凯 田鑫尧 HONG Baojian;ZHU Yongkang;QU Xinkai;TIAN Xinyao(School of Mathematical Physics,Nanjing Institute of Technology,Nanjing 211167,China;School of Electric Power Engineering,Nanjing Institute of Technology,Nanjing 211167,China)

机构地区：[1]南京工程学院数理学院,江苏南京211167 [2]南京工程学院电力工程学院,江苏南京211167

出　　处：《安徽大学学报（自然科学版）》2024年第6期21-29,共9页Journal of Anhui University(Natural Science Edition)

基　　金：江苏省高等学校自然科学研究项目(18KJB110013);江苏省大学生实践创新训练计划指导项目(202311276081Y)。

摘　　要：通过修正的(G'/G,1/G)-展开法,借助Mathematica软件,研究了一类在激光物理、等离子体物理等领域具有重要应用的广义时空分数阶耦合Zakharov方程组,求出了其一系列新的复合形式的解析解,这些解对于揭示高频波和低频波之间的非线性自相互作用,强湍流效应中Langmuir场的振幅、电磁波强度以及调幅的不稳定性演化过程具有重要意义.通过绘制出部分解对应的2,3维分布图及密度图,直观展示了相关物理量的演化过程,这些解丰富、简化和发展了已有的结果.In this article,with the aid of mathematica software,some new analytical solutions to a class of generalized time-space fractionalcoupled Zakharov equations which were important applications in laser physics,plasma physics and other fields were deeply studied by using the modified(G'/G,1/G)-expansion method,and a series of new composite forms of analytical solutions were obtained,which were essential for revealing the nonlinear self-interaction between high-frequency and low-frequency waves,the amplitude of Langmuir field in strong turbulence effects.The evolution process of electromagnetic wave intensity and amplitude modulation instability was of great significance,and the evolution process of related physical quantities was visually demonstrated by drawing the two-dimensional and three-dimensional plots and density maps corresponding to the partial solutions,which enriched,simplified and developed the existing results.

关 键 词：Atangana-Baleanu-Riemann分数阶导数 耦合Zakharov方程组 修正的(G'/G 1/G)-展开法 精确解 Mittag-Leffler函数 

分 类 号：O175.25[理学—数学]