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lump solution and interaction solutions to the fourth-order extended(2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

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Communications in Theoretical Physics 2023年第10期75卷 26-37页

作者： Wenxia Chen Yi Wang Lixin Tian Nonlinear Scientific Research Center Faculty of ScienceJiangsu UniversityZhenjiangJiangsu 212013China

In this paper,we explore the exact solutions to the fourth-order extended(2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation.Based on Hirota bilinear method,lump solution,periodic cross-kink solutions and bright-dark soliton solutions were investigated.By calculating and solving,the peak and trough of lump solution are obtained,and the maximum and minimum points of each are solved.The three-dimensional plots and density plots of periodic cross-kink solution and bright-dark soliton solution are drawn and the dynamics of solutions under different parameters are observed.

关键词： Hirota bilinear method eBLMP equation lump solution interation solution

Integrability and Exact solutions of the(2+1)-dimensional KdV Equation with Bell Polynomials Approach

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Acta Mathematicae Applicatae Sinica 2022年第4期38卷 861-881页

作者： Jun-cai PU Yong CHEN School of Mathematical Sciences Shanghai Key Laboratory of Pure Mathematics and Mathematical PracticeEast China Normal UniversityShanghai 200062China College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590China

In this paper,the bilinear formalism,bilinear B?cklund transformations and Lax pair of the(2+1)-dimensional KdV equation are constructed by the Bell polynomials approach.The N-soliton solution is derived directly from the bilinear form.Especially,based on the two-soliton solution,the lump solution is given out analytically by taking special parameters and using Taylor expansion formula.With the help of the multidimensional Riemann theta function,multiperiodic(quasiperiodic)wave solutions for the(2+1)-dimensional KdV equation are obtained by employing the Hirota bilinear method.Moreover,the asymptotic properties of the one-and two-periodic wave solution,which reveal the relations with the single and two-soliton solution,are presented in detail.

关键词： the bilinear formalism bilinear B?cklund transformations Lax pair lump solution periodic wave solution the asymptotic properties

lump,its interaction phenomena and conservation laws to a nonlinear mathematical model

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Journal of Ocean Engineering and Science 2022年第4期7卷 363-371页

作者： Abdullahi Yusuf Tukur Abdulkadir Sulaiman Evren Hincal Dumitru Baleanu Department of Computer Engineering Biruni UniversityIstanbulTurkey Department of Mathematics Near East University TRNCMersin 10Turkey Department of Mathematics Federal University DutseJigawaNigeria Department of Mathematics Cankaya UniversityAnkaraTurkey Institute of Space Sciences MagureleBucharestRomania Department of Medical Research China Medical University HospitalChina Medical UniversityTaichungTaiwan

We solve the Ostrovsky equation in the absence of the rotation effect using the Hirota bilinear method and symbolic calculation.Some unique interaction phenomena have been obtained between lump so-lution,breather wave,periodic wave,kink soliton,and two-wave solutions.All the obtained solutions are validated by putting them into the original problem using the Wolfram Mathematica 12.The physical characteristics of the solutions have been visually represented to shed additional light on the acquired re-sults.Furthermore,using the novel conservation theory,the conserved vectors of the governing equation have been generated.The discovered results are helpful in understanding particular physical phenomena in fluid dynamics as well as the dynamics of nonlinear higher dimensional wave fields in computational physics and ocean engineering and related disciplines.

关键词： lump solution New interaction phenomena Breather waves Symmetry analysis Conservation laws

lump solutions to a generalized Hietarinta-type equation via symbolic computation

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Frontiers of Mathematics in China 2020年第3期15卷 435-450页

作者： Sumayah BATWA Wen-Xiu MA Department of Mathematics King Abdulaziz UniversityJeddahSaudi Arabia Department of Mathematics Zhejiang Normal UniversityJinhua 321004China Department of Mathematics and Statistics University of South FloridaTampaFL 33620USA School of Mathematics South China University of TechnologyGuangzhou 510640China

lump solutions are one of important solutions to partial differential equations,both linear and nonlinear.This paper aims to show that a Hietarinta-type fourth-order nonlinear term can create lump solutions with second-order linear dispersive terms.The key is a Hirota bilinear form.lump solutions are constructed via symbolic computations with Maple,and specific reductions of the resulting lump solutions are made.Two illustrative examples of the generalized Hietarinta-type nonlinear equations and their lumps are presented,together with three-dimensional plots and density plots of the lump solutions.

关键词： Soliton equation lump solution symbolic computation Hirota derivative dispersion relation

lump solutions to a generalized Bogoyavlensky-Konopelchenko equation

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Frontiers of Mathematics in China 2018年第3期13卷 525-534页

作者： Shou-Ting CHEN Wen-Xiu MA School of Mathematics and Physical Science Xuzhou Institute of Technology Xuzhou 221008 China Department of Mathematics and Statistics University of South Florida Tampa FL 33620 USA College of Mathematics and Systems Science Shandong University of Science and Technology Qingdao 266590 China International Institute for Symmetry Analysis and Mathematical Modelling Department of Mathematical Sciences North-West University Mafikeng Campus Mmabatho 2735 South Africa

A （2 ＋ 1）-dimensional generalized Bogoyavlensky-Konopelchenko equation that possesses a Hirota bilinear form is considered. Starting with its Hirota bilinear form, a class of explicit lump solutions is computed through conducting symbolic computations with Maple, and a few plots of a specific presented lump solution are made to shed light on the characteristics of lumps. The result provides a new example of （2 ＋ 1）-dimensional nonlinear partial differential equations which possess lump solutions.

关键词： Symbolic computation lump solution soliton theory

lump solutions and Interaction Phenomenon for (2+1)-Dimensional Sawada–Kotera Equation

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Communications in Theoretical Physics 2017年第5期67卷 473-478页

作者：黄丽丽陈勇 Shanghai Key Laboratory of Trustworthy Computing East China Normal University Shanghai 200062 China MOE International Joint Lab of Trustworthy Software East China Normal University Shanghai 200062 China

In this paper, a class of lump solutions to the (2+1)-dimensional Sawada–Kotera equation is studied by searching for positive quadratic function solutions to the associated bilinear equation. To guarantee rational localization and analyticity of the lumps, some sufficient and necessary conditions are presented on the parameters involved in the solutions. Then, a completely non-elastic interaction between a lump and a stripe of the(2+1)-dimensional Sawada–Kotera equation is obtained, which shows a lump solution is drowned or swallowed by a stripe soliton. Finally, 2-dimensional curves, 3-dimensional plots and density plots with particular choices of the involved parameters are presented to show the dynamic characteristics of the obtained lump and interaction solutions.

关键词： lump solution interaction solution Hirota bilinear method (2+1)-dimensional Sawada–Kotera equation

Interaction solutions for the second extended(3+1)-dimensional Jimbo–Miwa equation

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Chinese Physics B 2023年第6期32卷 112-121页

作者：马红彩毛雪邓爱平 Department of Applied Mathematics Donghua UniversityShanghai 201620China

Based on the Hirota bilinear method,the second extended(3+1)-dimensional Jimbo–Miwa equation is established.By Maple symbolic calculation,lump and lump-kink soliton solutions are obtained.The interaction solutions between the lump and multi-kink soliton,and the interaction between the lump and triangular periodic soliton are derived by combining a multi-exponential function or trigonometric sine and cosine functions with quadratic functions.Furthermore,periodiclump wave solution is derived via the ansatz including hyperbolic and trigonometric functions.Finally,3D plots,2D curves,density plots,and contour plots with particular choices of the suitable parameters are depicted to illustrate the dynamical features of these solutions.

关键词： Hirota bilinear method second extended(3+1)-dimensional Jimbo–Miwa equation lump solution interaction solution

From breather solutions to lump solutions:A construction method for the Zakharov equation

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Chinese Physics B 2023年第12期32卷 162-169页

作者：袁丰 Behzad Ghanbari 张永帅 Abdul Majid Wazwaz College of Science Nanjing University of Posts and TelecommunicationsNanjing 210023China Department of Mathematics Kermanshah University of TechnologyKermanshahIran Department of Mathematics Shaoxing UniversityShaoxing 312000China Department of Mathematics Saint Xavier UniversityChicagoIL 60655USA

Periodic solutions of the Zakharov equation are investigated.By performing the limit operationλ_(2l-1)→λ_(1)on the eigenvalues of the Lax pair obtained from the n-fold Darboux transformation,an order-n breather-positon solution is first obtained from a plane wave seed.It is then proven that an order-n lump solution can be further constructed by taking the limitλ_(1)→λ_(0)on the breather-positon solution,because the unique eigenvalueλ_(0)associated with the Lax pair eigenfunctionΨ(λ_(0))=0 corresponds to the limit of the infinite-periodic solutions.A convenient procedure of generating higher-order lump solutions of the Zakharov equation is also investigated based on the idea of the degeneration of double eigenvalues in multi-breather solutions.

关键词： Zakharov equation breather solution b-positon solution lump solution

Dynamics of mixed lump-soliton for an extended(2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov equation

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Communications in Theoretical Physics 2022年第3期74卷 1-10页

作者： Kai-Zhong Shi Shou-Feng Shen Bo Ren Wan-Li Wang Department of Mathematics Zhejiang University of TechnologyHangzhou 310014China

A new(2+1)-dimensional higher-order extended asymmetric Nizhnik-Novikov-Veselov(eANNV)equation is proposed by introducing the additional bilinear terms to the usual ANNV equation.Based on the independent transformation,the bilinear form of the eANNV equation is constructed.The lump wave is guaranteed by introducing a positive constant term in the quadratic function.Meanwhile,different class solutions of the eANNV equation are obtained by mixing the quadratic function with the exponential functions.For the interaction between the lump wave and one-soliton,the energy of the lump wave and one-soliton can transfer to each other at different times.The interaction between a lump and two-soliton can be obtained only by eliminating the sixth-order bilinear term.The dynamics of these solutions are illustrated by selecting the specific parameters in three-dimensional,contour and density plots.

关键词： Extended ANNV equation Hirota bilinear method lump solution