(2+1)维广义Hietarinta-type方程的呼吸解和高阶lump-type解  

Breather wave solutions and high-order lump-type solutions of the(2+1)dimensional generalized Hietarinta-type equation

作　　者：韩莉慧 苏道毕力格[1] 李美玉 HAN Lihui;SU Daobilige;LI Meiyu(School of Science,Inner Mongolia University of Technology,Hohhot 010051,China;School of Mathematics and Statistics,Institute of Hulunbuir,Hulunbuir 021009,China)

机构地区：[1]内蒙古工业大学理学院,呼和浩特010051 [2]呼伦贝尔学院数学与统计学院,内蒙古呼伦贝尔021009

出　　处：《内蒙古工业大学学报（自然科学版）》2023年第4期289-293,共5页Journal of Inner Mongolia University of Technology：Natural Science Edition

基　　金：国家自然科学基金项目(12061054);内蒙古自治区大学青年科技人才计划项目(NJYT-20-A06);内蒙古自治区自然科学基金项目(2018LH01013)。

摘　　要：为了构造(2+1)维广义Hietarinta-type方程丰富的精确解,基于Hirota双线性方法研究该方程。Hirota双线性方法是一种求非线性发展方程孤子解的简单而直接的代数方法。近年来该方法已经在构造非线性发展方程精确解的研究领域上得到了广泛的应用。基于该方法,构造非线性发展方程的非线性波对数学、物理、力学等学科中的高维非线性问题的研究有非常重要的理论和应用价值。利用Hirota双线性方法给出了(2+1)维广义Hietarinta-type方程的双线性形式,并运用符号计算软件Maple获得了该方程的呼吸解和高阶lump-type解。再通过选择适当的参数,绘制了这些解的三维图、等高线图和密度图,并分析和描述了解的动力学性质。这些结果丰富了目前关于(2+1)维广义Hietarinta-type方程文献中的结果。In order to construct rich exact solutions for the(2+1)dimensional generalized Hietarinta-type equation,we investigated this equation using the Hirota bilinear method,which is a simple and direct algebraic method for obtaining soliton solutions of nonlinear evolution equations and has been widely applied in the study of constructing exact solutions.Using this method to construct nonlinear wave equations has significant theoretical and practical value for the study of high-dimensional nonlinear problems in mathematics,physics and mechanics.The bilinear form of the(2+1)dimensional generalized Hietarinta-type equation was derived by using the Hirota bilinear method,and the breather wave solutions and high-order lump-type solutions were obtained by using the symbolic computing software Maple.By selecting appropriate parameters,the three-dimensional plots,contour plots,and density plots of these solutions were drawn,and their dynamics properties were analyzed and described.

关 键 词：(2+1)维广义Hietarinta-type方程 双线性形式 呼吸解 高阶lump-type解 

分 类 号：O175.2[理学—数学]