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广义(3+1)维KP方程的精确有理解
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作者 胡英武 《金华职业技术学院学报》 2023年第6期70-73,共4页
利用Hirota方法及Maple,得到了一类带9个二阶导数项的(3+1)维KP方程的精确有理解。在一定条件下,方程有lump型解,解中有八个自由参数,在特定参数下,通过定量与作图分析给出了解的数值模拟。
关键词 广义(3+1)维KP方程 HIROTA方法 有理解 lump型解
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Integrability Tests and Some New Soliton Solutions of an Extended Potential Boiti-Leon-Manna-Pempinelli Equation
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作者 Miao Li Wei Tan Houping Dai 《Journal of Applied Mathematics and Physics》 2022年第10期2895-2905,共11页
This paper is devoted to the study of a (2 + 1)-dimensional extended Potential Boiti-Leon-Manna-Pempinelli equation. Firstly, By means of the standard Weiss Tabor Carnevale approach and Kruskal’s simplification, we p... This paper is devoted to the study of a (2 + 1)-dimensional extended Potential Boiti-Leon-Manna-Pempinelli equation. Firstly, By means of the standard Weiss Tabor Carnevale approach and Kruskal’s simplification, we prove the painlevé non integrability of the equation. Secondly, A new breather solution and lump type solution are obtained based on the parameter limit method and Hirota’s bilinear method. Besides, some interaction behavior between lump type solution and N-soliton solutions (N is any positive integer) are studied. We construct the existence theorem of the interaction solution and give the process of calculation and proof. We also give a concrete example to illustrate the effectiveness of the theorem, and some spatial structure figures are displayed to reflect the evolutionary behavior of the interaction solutions with the change of soliton number N and time t. 展开更多
关键词 BLMP Equation lump type solution Interaction Behavior Parameter Limit Method Hirota’s Bilinear Method
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Lump-type solutions of a generalized Kadomtsev–Petviashvili equation in(3+1)-dimensions 被引量:1
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作者 Xue-Ping Cheng Wen-Xiu Ma Yun-Qing Yang 《Chinese Physics B》 SCIE EI CAS CSCD 2019年第10期245-252,共8页
Through the Hirota bilinear formulation and the symbolic computation software Maple, we construct lump-type solutions for a generalized(3+1)-dimensional Kadomtsev-Petviashvili(KP) equation in three cases of the coeffi... Through the Hirota bilinear formulation and the symbolic computation software Maple, we construct lump-type solutions for a generalized(3+1)-dimensional Kadomtsev-Petviashvili(KP) equation in three cases of the coefficients in the equation. Then the sufficient and necessary conditions to guarantee the analyticity of the resulting lump-type solutions(or the positivity of the corresponding quadratic solutions to the associated bilinear equation) are discussed. To illustrate the generality of the obtained solutions, two concrete lump-type solutions are explicitly presented, and to analyze the dynamic behaviors of the solutions specifically, the three-dimensional plots and contour profiles of these two lump-type solutions with particular choices of the involved free parameters are well displayed. 展开更多
关键词 lump-type solution generalized(3+1)-dimensional Kadomtsev-Petviashvili equation HIROTA bilinear form symbolic computation
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(2+1)维广义Hietarinta-type方程的呼吸解和高阶lump-type解
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作者 韩莉慧 苏道毕力格 李美玉 《内蒙古工业大学学报(自然科学版)》 2023年第4期289-293,共5页
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... 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。 展开更多
关键词 (2+1)维广义Hietarinta-type方程 双线性形式 呼吸解 高阶lump-type
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