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Bifurcations, Analytical and Non-Analytical Traveling Wave Solutions of (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation
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作者 Dahe Feng Jibin Li Airen Zhou 《Applied Mathematics》 2024年第8期543-567,共25页
For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits ... For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation. 展开更多
关键词 (2 + 1)-dimensional Nonlinear Dispersive Boussinesq equation BIFURCATIONS Phase Portrait Analytical Periodic Wave Solution Periodic Cusp Wave Solution
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New periodic wave solutions, localized excitations and their interaction for (2+1)-dimensional Burgers equation 被引量:2
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作者 马红彩 葛东杰 于耀东 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第12期4344-4353,共10页
Based on the B/icklund method and the multilinear variable separation approach (MLVSA), this paper finds a general solution including two arbitrary functions for the (2+1)-dimensional Burgers equations. Then a cl... Based on the B/icklund method and the multilinear variable separation approach (MLVSA), this paper finds a general solution including two arbitrary functions for the (2+1)-dimensional Burgers equations. Then a class of new doubly periodic wave solutions for (2+l)-dimensional Burgers equations is obtained by introducing appropriate Jacobi elliptic functions, Weierstrass elliptic functions and their combination in the general solutions (which contains two arbitrary functions). Two types of limit cases are considered. Firstly, taking one of the moduli to be unity and the other zero, it obtains particular wave (called semi-localized) patterns, which is periodic in one direction, but localized in the other direction. Secondly, if both moduli are tending to 1 as a limit, it derives some novel localized excitations (two-dromion solution). 展开更多
关键词 2+1)-dimensional burgers equation mutilinear variable separation approach periodicwave solutions localized excitation
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Decay Mode Solutions to (2 + 1)-Dimensional Burgers Equation, Cylindrical Burgers Equation and Spherical Burgers Equation 被引量:1
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作者 Xiangzheng Li Jinliang Zhang Mingliang Wang 《Journal of Applied Mathematics and Physics》 2017年第5期1009-1015,共7页
Three (2 + 1)-dimensional equations—Burgers equation, cylindrical Burgers equation and spherical Burgers equation, have been reduced to the classical Burgers equation by different transformation of variables respecti... Three (2 + 1)-dimensional equations—Burgers equation, cylindrical Burgers equation and spherical Burgers equation, have been reduced to the classical Burgers equation by different transformation of variables respectively. The decay mode solutions of the Burgers equation have been obtained by using the extended -expansion method, substituting the solutions obtained into the corresponding transformation of variables, the decay mode solutions of the three (2 + 1)-dimensional equations have been obtained successfully. 展开更多
关键词 DECAY mode Solution (2 + 1)-burgers equation (2 + 1)-Cylindrical burgers equation (2 + 1)-Spherical burgers equation Transformation of Variables Extended (G'/G)-Expansion Method
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New Complexiton Solutions for the(2+1)-dimensional Burgers Equation
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作者 李文婷 陈续升 张鸿庆 《Northeastern Mathematical Journal》 CSCD 2007年第5期453-463,共11页
In this paper, a new generalized compound Riccati equations rational expansion method (GCRERE) is proposed. Compared with most existing rational expansion methods and other sophisticated methods, the proposed method... In this paper, a new generalized compound Riccati equations rational expansion method (GCRERE) is proposed. Compared with most existing rational expansion methods and other sophisticated methods, the proposed method is not only recover some known solutions, but also find some new and general complexiton solutions. Being concise and straightforward, it is applied to the (2+1)-dimensional Burgers equation. As a result, eight families of new exact analytical solutions for this equation are found. The method can also be applied to other nonlinear partial differential equations. 展开更多
关键词 generalized compound Riccati equations rational expansion method 2+1)-dimensional burgers equation complexiton solution
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Interactions among special embed-solitons for the (3+1)-dimensional Burgers equation 被引量:1
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作者 张雯婷 戴朝卿 陈未路 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第4期196-199,共4页
With the help of a modified mapping method and a new mapping method, we re-study the (3+1)-dimensional Burgers equation, and derive two families of variable separation solutions. By selecting appropriate functions ... With the help of a modified mapping method and a new mapping method, we re-study the (3+1)-dimensional Burgers equation, and derive two families of variable separation solutions. By selecting appropriate functions in the variable separation solution, we discuss the interaction behaviors among taper-like, plateau-type rings, and rectangle-type embed-solitons in the periodic wave background. All the interaction behaviors are completely elastic, and no phase shift appears after interaction. 展开更多
关键词 (3+1)-dimensional burgers equation modified mapping method interaction between special embed-solitons
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Lump and interaction solutions to the (3+1)-dimensional Burgers equation
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作者 Jian Liu Jian-Wen Wu 《Chinese Physics B》 SCIE EI CAS CSCD 2020年第3期50-54,共5页
The(3+1)-dimensional Burgers equation, which describes nonlinear waves in turbulence and the interface dynamics,is considered. Two types of semi-rational solutions, namely, the lump–kink solution and the lump–two ki... The(3+1)-dimensional Burgers equation, which describes nonlinear waves in turbulence and the interface dynamics,is considered. Two types of semi-rational solutions, namely, the lump–kink solution and the lump–two kinks solution, are constructed from the quadratic function ansatz. Some interesting features of interactions between lumps and other solitons are revealed analytically and shown graphically, such as fusion and fission processes. 展开更多
关键词 (3+1)-dimensional burgers equation lump SOLUTION INTERACTION wave SOLUTION BILINEAR form
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The Travelling Wave Solutions for (2+1)-dimensional AKNS Equation 被引量:3
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作者 程智龙 郝晓红 《Chinese Quarterly Journal of Mathematics》 2015年第3期323-329,共7页
Based on the travelling wave method, a(2 + 1)-dimensional AKNS equation is considered. Elliptic solution and soliton solution are presented and it is shown that the soliton solution can be reduced from the elliptic so... Based on the travelling wave method, a(2 + 1)-dimensional AKNS equation is considered. Elliptic solution and soliton solution are presented and it is shown that the soliton solution can be reduced from the elliptic solution. It also proves that the result is consistent with the soliton solution of simplify Hirota bilinear method by Wazwaz and illustrate the solution are right travelling wave solution. 展开更多
关键词 (2+1)-dimensional AKNS equation SOLITON SOLUTION
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New exact periodic solutions to (2+1)-dimensional dispersive long wave equations 被引量:2
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作者 张文亮 吴国将 +2 位作者 张苗 王军帽 韩家骅 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第4期1156-1164,共9页
In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for (2+1)-dimensional dispersive long wave equations in mathematical physics, which are... In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for (2+1)-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions (m → 1). This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations. 展开更多
关键词 auxiliary equation method expanded mapping method 2+1)-dimensional dispersivelong wave equations periodic wave solutions
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Nonlocal symmetry and exact solutions of the(2+1)-dimensional modified Bogoyavlenskii–Schiff equation 被引量:3
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作者 黄丽丽 陈勇 《Chinese Physics B》 SCIE EI CAS CSCD 2016年第6期63-70,共8页
In this paper,the truncated Painlev′e analysis,nonlocal symmetry,Bcklund transformation of the(2+1)-dimensional modified Bogoyavlenskii–Schiff equation are presented.Then the nonlocal symmetry is localized to the... In this paper,the truncated Painlev′e analysis,nonlocal symmetry,Bcklund transformation of the(2+1)-dimensional modified Bogoyavlenskii–Schiff equation are presented.Then the nonlocal symmetry is localized to the corresponding nonlocal group by the prolonged system.In addition,the(2+1)-dimensional modified Bogoyavlenskii–Schiff is proved consistent Riccati expansion(CRE) solvable.As a result,the soliton–cnoidal wave interaction solutions of the equation are explicitly given,which are difficult to find by other traditional methods.Moreover figures are given out to show the properties of the explicit analytic interaction solutions. 展开更多
关键词 2+1)-dimensional modified Bogoyavlenskii–Schiff equation nonlocal symmetry consistent Riccati expansion soliton–cnoidal wave solution
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The exact solutions to (2+1)-dimensional nonlinear Schrdinger equation 被引量:4
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作者 ZHANGJin-liang WANGMing-liang FANGZong-de 《原子与分子物理学报》 CAS CSCD 北大核心 2004年第1期78-82,共5页
By using the extended F-expansion method, the exact solutions,including periodic wave solutions expressed by Jacobi elliptic functions, for (2+1)-dimensional nonlinear Schrdinger equation are derived. In the limit c... By using the extended F-expansion method, the exact solutions,including periodic wave solutions expressed by Jacobi elliptic functions, for (2+1)-dimensional nonlinear Schrdinger equation are derived. In the limit cases, the solitary wave solutions and the other type of traveling wave solutions for the system are obtained. 展开更多
关键词 非线性薛定谔方程 精确解 行波解 孤波解 周期波解 计算物理学
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Exact solutions of a(2+1)-dimensional extended shallow water wave equation 被引量:1
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作者 Feng Yuan Jing-Song He Yi Cheng 《Chinese Physics B》 SCIE EI CAS CSCD 2019年第10期237-244,共8页
We give the bilinear form and n-soliton solutions of a(2+1)-dimensional [(2+1)-D] extended shallow water wave(eSWW) equation associated with two functions v and r by using Hirota bilinear method. We provide soli... We give the bilinear form and n-soliton solutions of a(2+1)-dimensional [(2+1)-D] extended shallow water wave(eSWW) equation associated with two functions v and r by using Hirota bilinear method. We provide solitons, breathers,and hybrid solutions of them. Four cases of a crucial φ(y), which is an arbitrary real continuous function appeared in f of bilinear form, are selected by using Jacobi elliptic functions, which yield a periodic solution and three kinds of doubly localized dormion-type solution. The first order Jacobi-type solution travels parallelly along the x axis with the velocity(3k12+ α, 0) on(x, y)-plane. If φ(y) = sn(y, 3/10), it is a periodic solution. If φ(y) = cn(y, 1), it is a dormion-type-Ⅰ solutions which has a maximum(3/4)k1p1 and a minimum-(3/4)k1p1. The width of the contour line is ln■. If φ(y) = sn(y, 1), we get a dormion-type-Ⅱ solution(26) which has only one extreme value-(3/2)k1p1. The width of the contour line is ln■. If φ(y) = sn(y, 1/2)/(1 + y2), we get a dormion-type-Ⅲ solution(21) which shows very strong doubly localized feature on(x, y) plane. Moreover, several interesting patterns of the mixture of periodic and localized solutions are also given in graphic way. 展开更多
关键词 (2+1)-dimensional EXTENDED shallow water wave equation HIROTA BILINEAR method dormion-type solution
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Painlevé Property and Exact Solutions to a (2+1) Dimensional KdV-mKdV Equation 被引量:1
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作者 Yuqing Liu Fang Duan Chao Hu 《Journal of Applied Mathematics and Physics》 2015年第6期697-706,共10页
A (2 + 1) dimensional KdV-mKdV equation is proposed and integrability in the sense of Painlevé and some exact solutions are discussed. The B?cklund transformation and bilinear equations are obtained through Painl... A (2 + 1) dimensional KdV-mKdV equation is proposed and integrability in the sense of Painlevé and some exact solutions are discussed. The B?cklund transformation and bilinear equations are obtained through Painlevé analysis. Some exact solutions are deduced by Hirota method and generalized Wronskian method. 展开更多
关键词 (2+1) dimensional KdV-mKdV equation Painlevé Property Backlund Transformation Bilinear equation Wronskian Method
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New Exact Solutions of the (2 + 1)-Dimensional AKNS Equation 被引量:1
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作者 Yepeng Sun 《Journal of Applied Mathematics and Physics》 2015年第11期1391-1405,共15页
N-soliton solutions and the bilinear form of the (2 + 1)-dimensional AKNS equation are obtained by using the Hirota method. Moreover, the double Wronskian solution and generalized double Wronskian solution are constru... N-soliton solutions and the bilinear form of the (2 + 1)-dimensional AKNS equation are obtained by using the Hirota method. Moreover, the double Wronskian solution and generalized double Wronskian solution are constructed through the Wronskian technique. Furthermore, rational solutions, Matveev solutions and complexitons of the (2 + 1)-dimensional AKNS equation are given through a matrix method for constructing double Wronskian entries. The three solutions are new. 展开更多
关键词 (2 + 1)-dimensional AKNS equation RATIONAL SOLUTIONS Matveev SOLUTIONS Complexitons
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Solving (2+1)-dimensional sine-Poisson equation by a modified variable separated ordinary differential equation method 被引量:1
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作者 苏卡林 谢元喜 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第10期40-48,共9页
By introducing a more general auxiliary ordinary differential equation (ODE), a modified variable separated ordinary differential equation method is presented for solving the (2 + 1)-dimensional sine-Poisson equa... By introducing a more general auxiliary ordinary differential equation (ODE), a modified variable separated ordinary differential equation method is presented for solving the (2 + 1)-dimensional sine-Poisson equation. As a result, many explicit and exact solutions of the (2 + 1)-dimensional sine-Poisson equation are derived in a simple manner by this technique. 展开更多
关键词 modified variable separated ODE method 2 1)-dimensional sine-Poisson equation explicit and exact solution
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New Exact Traveling Wave Solutions of (2 + 1)-Dimensional Time-Fractional Zoomeron Equation 被引量:2
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作者 Zhiyun Zeng Xiaohua Liu +1 位作者 Yin Zhu Xue Huang 《Journal of Applied Mathematics and Physics》 2022年第2期333-346,共14页
In this paper, the new mapping approach and the new extended auxiliary equation approach were used to investigate the exact traveling wave solutions of (2 + 1)-dimensional time-fractional Zoomeron equation with the co... In this paper, the new mapping approach and the new extended auxiliary equation approach were used to investigate the exact traveling wave solutions of (2 + 1)-dimensional time-fractional Zoomeron equation with the conformable fractional derivative. As a result, the singular soliton solutions, kink and anti-kink soliton solutions, periodic function soliton solutions, Jacobi elliptic function solutions and hyperbolic function solutions of (2 + 1)-dimensional time-fractional Zoomeron equation were obtained. Finally, the 3D and 2D graphs of some solutions were drawn by setting the suitable values of parameters with Maple, and analyze the dynamic behaviors of the solutions. 展开更多
关键词 Exact Traveling Wave Solutions (2 + 1)-dimensional Time-Fractional Zoomeron equation The New Mapping Approach The New Extended Auxiliary equation Approach
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An Invariance for (2+1)-Extension of Burgers Equation and Formulae to Obtain Solutions of KP Equation
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作者 TIANYong-Bo TIANChou SHAONan 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第4期591-596,共6页
In this article, we study the (2+1)-extension of Burgers equation and the KPequation. At first, based on a known Baecklund transformation and corresponding Lax pair, aninvariance which depends on two arbitrary functio... In this article, we study the (2+1)-extension of Burgers equation and the KPequation. At first, based on a known Baecklund transformation and corresponding Lax pair, aninvariance which depends on two arbitrary functions for (2+1)-extension of Burgers equation isworked out. Given a known solution and using the invariance, we can find solutions of the(2+1)-extension of Burgers equation repeatedly. Secondly, we put forward an invariance of Burgersequation which cannot be directly obtained by constraining the invariance of the (2+1)-extension ofBurgers equation. Furthermore, we reveal that the invariance for finding the solutions of Burgersequation can help us find the solutions of KP equation. At last, based on the invariance of Burgersequation, the corresponding recursion formulae for finding solutions of KP equation are digged out.As the application of our theory, some examples have been put forward in this article and somesolutions of the (2+1)-extension of Burgers equation, Burgers equation and KP equation are obtained. 展开更多
关键词 invariance (2+1)-extension of burgers equation formulae for obtainingsolutions of KP equation
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Wronskian and Grammian solutions for the(2+1)-dimensional BKP equation
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作者 Yaning Tang Yanna Chen Lei Wang 《Theoretical & Applied Mechanics Letters》 CAS 2014年第1期73-76,共4页
The (2+1)-dimensional BKP equation in the Hirota bilinear form is studied during this work. Wronskian and Grammian techniques are applied to the construction of Wronskian and Grammian solutions of this equation, re... The (2+1)-dimensional BKP equation in the Hirota bilinear form is studied during this work. Wronskian and Grammian techniques are applied to the construction of Wronskian and Grammian solutions of this equation, respectively. It is shown that these solutions can be expressed as not only Pfaffians but also Wronskians and Grammians. 展开更多
关键词 2+1)-dimensional BKP equation Wronskian solution Grammian solution
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Truncated series solutions to the(2+1)-dimensional perturbed Boussinesq equation by using the approximate symmetry method
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作者 Xiao-Yu Jiao 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第10期123-129,共7页
In this paper, the(2+1)-dimensional perturbed Boussinesq equation is transformed into a series of two-dimensional(2 D) similarity reduction equations by using the approximate symmetry method. A step-by-step proce... In this paper, the(2+1)-dimensional perturbed Boussinesq equation is transformed into a series of two-dimensional(2 D) similarity reduction equations by using the approximate symmetry method. A step-by-step procedure is used to acquire Jacobi elliptic function solutions to these similarity equations, which generate the truncated series solutions to the original perturbed Boussinesq equation. Aside from some singular area, the series solutions are convergent when the perturbation parameter is diminished. 展开更多
关键词 approximate symmetry method 2+1)-dimensional perturbed Boussinesq equation series solutions convergence of series solutions
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Exact Solutions for (2 + 1)-Dimensional KdV-Calogero-Bogoyavlenkskii-Schiff Equation via Symbolic Computation
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作者 Yan Li Temuer Chaolu 《Journal of Applied Mathematics and Physics》 2020年第2期197-209,共13页
This paper constructs exact solutions for the (2 + 1)-dimensional KdV-Calogero-Bogoyavlenkskii-Schiff equation with the help of symbolic computation. By means of the truncated Painlev expansion, the (2 + 1)-dimensiona... This paper constructs exact solutions for the (2 + 1)-dimensional KdV-Calogero-Bogoyavlenkskii-Schiff equation with the help of symbolic computation. By means of the truncated Painlev expansion, the (2 + 1)-dimensional KdV-Calogero-Bogoyavlenkskii-Schiff equation can be written as a trilinear equation, through the trilinear-linear equation, we can obtain the explicit representation of exact solutions for the (2 + 1)-dimensional KdV-Calogero-Bogoyavlenkskii-Schiff equation. We have depicted the profiles of the exact solutions by presenting their three-dimensional plots and the corresponding density plots. 展开更多
关键词 (2 + 1)-dimensional KdV-Calogero-Bogoyavlenkskii-Schiff equation Trilinear equation Exact Solutions
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Diversity of Interaction Solutions to the (2 + 1)-Dimensional Sawada-Kotera Equation
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作者 Rui Hu 《Journal of Applied Mathematics and Physics》 2018年第8期1692-1703,共12页
In this paper, based on Hirota bilinear form, we aim to show the diversity of interaction solutions to the (2 + 1)-dimensional Sawada-Kotera (SK) equation. By introducing an arbitrary differentiable function in assump... In this paper, based on Hirota bilinear form, we aim to show the diversity of interaction solutions to the (2 + 1)-dimensional Sawada-Kotera (SK) equation. By introducing an arbitrary differentiable function in assumption form, we can obtain abundant interaction solutions which can provide the possibility for exploring the interactions between lump waves and other kinds of waves. By choosing some particular functions and values of the involved parameters, we give four illustrative examples of the resulting solutions, and explore some novel interaction behaviors in (2 + 1)-dimensional SK equation. 展开更多
关键词 HIROTA BILINEAR Form Lump SOLUTION INTERACTION SOLUTION (2 + 1)-dimensional Sawada-Kotera equation
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