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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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Riemann theta function periodic wave solutions for the variable-coefficient mKdV equation 被引量:1
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作者 张翼 程智龙 郝晓红 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第12期23-30,共8页
In this paper, a variable-coefficient modified Korteweg-de Vries (vc-mKdV) equation is considered. Bilinear forms are presented to explicitly construct periodic wave solutions based on a multidimensional Riemann the... In this paper, a variable-coefficient modified Korteweg-de Vries (vc-mKdV) equation is considered. Bilinear forms are presented to explicitly construct periodic wave solutions based on a multidimensional Riemann theta function, then the one and two periodic wave solutions are presented~ and it is also shown that the soliton solutions can be reduced from the periodic wave solutions. 展开更多
关键词 variable-coefficient mKdV equation Riemann theta function soliton solutions periodic wave solutions
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Exact explicit solitary wave and periodic wave solutions and their dynamical behaviors for the Schamel–Korteweg–de Vries equation
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作者 何斌 蒙清 《Chinese Physics B》 SCIE EI CAS CSCD 2021年第6期62-76,共15页
The Schamel–Korteweg–de Vries equation is investigated by the approach of dynamics.The existences of solitary wave including ω-shape solitary wave and periodic wave are proved via investigating the dynamical behavi... The Schamel–Korteweg–de Vries equation is investigated by the approach of dynamics.The existences of solitary wave including ω-shape solitary wave and periodic wave are proved via investigating the dynamical behaviors with phase space analyses.The sufficient conditions to guarantee the existences of the above solutions in different regions of the parametric space are given.All possible exact explicit parametric representations of the waves are also presented.Along with the details of the analyses,the analytical results are numerically simulated lastly. 展开更多
关键词 Schamel–Korteweg–de Vries equation dynamical behavior solitary wave solution periodic wave solution
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EXISTENCE OF PERIODIC TRAVELNG WAVE SOLUTIONS FOR A CLASS OF GENERALIZED BBM EQUATION
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作者 黄南京 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1997年第6期599-603,共5页
In this paper. a new kind of generalized BBM equation is introduced and discussed Some existence theorems of periodic traveling wave solutions for this kind generalized BBM equation are given.
关键词 generalized BBM equation periodic traveling wave solution Green function fixed point
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Integrability, Multi-Solitary Wave Solutions and Riemann Theta Functions Periodic Wave Solutions of the Newell Equation
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作者 Chunmei Fang 《Journal of Applied Mathematics and Physics》 2022年第2期415-424,共10页
This paper systematically studies the complete integrability of the Newell equation. Using generalized Bell polynomials, the corresponding bilinear equation, bilinear B&#228;cklund transformation, Lax pair, and mu... This paper systematically studies the complete integrability of the Newell equation. Using generalized Bell polynomials, the corresponding bilinear equation, bilinear B&#228;cklund transformation, Lax pair, and multi-shock wave solutions are successfully obtained. In addition, using the multidimensional Riemann theta functions, the periodic wave solutions of the Newell equation are constructed. On this basis, the asymptotic behavior of the periodic wave solution is given, which is the relationship between the periodic wave solution and the solitary wave solution. 展开更多
关键词 The Newell Equation Bäcklund Transformation Lax Pair Solitary wave solution periodic wave solution
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Periodic Wave Solutions and Solitary Wave Solutions of the (2+1)-Dimensional Korteweg-de-Vries Equatio
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作者 Liangwei He Shuanghong Chen 《American Journal of Computational Mathematics》 2021年第4期327-339,共13页
In this paper, we investigate the periodic wave solutions and solitary wave solutions of a (2+1)-dimensional Korteweg-de Vries (KDV) equation</span><span style="font-size:10pt;font-family:"">... In this paper, we investigate the periodic wave solutions and solitary wave solutions of a (2+1)-dimensional Korteweg-de Vries (KDV) equation</span><span style="font-size:10pt;font-family:""> </span><span style="font-size:10pt;font-family:"">by applying Jacobi elliptic function expansion method. Abundant types of Jacobi elliptic function solutions are obtained by choosing different </span><span style="font-size:10.0pt;font-family:"">coefficient</span><span style="font-size:10.0pt;font-family:"">s</span><span style="font-size:10pt;font-family:""> <i>p</i>, <i>q</i> and <i>r</i> in the</span><span style="font-size:10pt;font-family:""> </span><span style="font-size:10pt;font-family:"">elliptic equation. Then these solutions are</span><span style="font-size:10pt;font-family:""> </span><span style="font-size:10pt;font-family:"">coupled into an auxiliary equation</span><span style="font-size:10pt;font-family:""> </span><span style="font-size:10pt;font-family:"">and substituted into the (2+1)-dimensional KDV equation. As <span>a result,</span></span><span style="font-size:10pt;font-family:""> </span><span style="font-size:10pt;font-family:"">a large number of complex Jacobi elliptic function solutions are ob</span><span style="font-size:10pt;font-family:"">tained, and many of them have not been found in other documents. As</span><span style="font-size:10pt;font-family:""> </span><span style="font-size:10.0pt;font-family:""><span></span></span><span style="font-size:10pt;font-family:"">, some complex solitary solutions are also obtained correspondingly.</span><span style="font-size:10pt;font-family:""> </span><span style="font-size:10pt;font-family:"">These solutions that we obtained in this paper will be helpful to understand the physics of the (2+1)-dimensional KDV equation. 展开更多
关键词 Nonlinear Evolution Equations Jacobi Elliptic Function (2+1)-Dimensional KDV periodic wave solutions Solitary wave Solu-tions
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BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS FOR THE GENERALIZED DODD-BULLOUGH-MIKHAILOV EQUATION 被引量:7
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作者 Tang Shengqiang Huang Wentao 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2007年第1期21-28,共8页
In this paper, the generalized Dodd-Bullough-Mikhailov equation is studied. The existence of periodic wave and unbounded wave solutions is proved by using the method of bifurcation theory of dynamical systems. Under d... In this paper, the generalized Dodd-Bullough-Mikhailov equation is studied. The existence of periodic wave and unbounded wave solutions is proved by using the method of bifurcation theory of dynamical systems. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.Some exact explicit parametric representations of the above travelling solutions are obtained. 展开更多
关键词 unbounded travelling wave solution periodic travelling wave solution the generalized Dodd- Bullough-Mikhailov equation.
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Analytical and Traveling Wave Solutions to the Fifth Order Standard Sawada-Kotera Equation via the Generalized exp(-Φ(ξ))-Expansion Method 被引量:1
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作者 M. Y. Ali M. G. Hafez +1 位作者 M. K. H. Chowdury M. T. Akter 《Journal of Applied Mathematics and Physics》 2016年第2期262-271,共10页
In this article, we propose a generalized exp(-Φ(ξ))-expansion method and successfully implement it to find exact traveling wave solutions to the fifth order standard Sawada-Kotera (SK) equation. The exact traveling... In this article, we propose a generalized exp(-Φ(ξ))-expansion method and successfully implement it to find exact traveling wave solutions to the fifth order standard Sawada-Kotera (SK) equation. The exact traveling wave solutions are established in the form of trigonometric, hyperbolic, exponential and rational functions with some free parameters. It is shown that this method is standard, effective and easily applicable mathematical tool for solving nonlinear partial differential equations arises in the field of mathematical physics and engineering. 展开更多
关键词 Generalized exp(-Φ(ξ))-Expansion Method Fifth Order Standard Sawada-Kotera Equation SOLITONS periodic wave solutions
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Exact traveling wave solutions to 2D-generalized Benney-Luke equation
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作者 李继彬 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第11期1391-1398,共8页
By using the dynamical system method to study the 2D-generalized Benney- Luke equation, the existence of kink wave solutions and uncountably infinite many smooth periodic wave solutions is shown. Explicit exact parame... By using the dynamical system method to study the 2D-generalized Benney- Luke equation, the existence of kink wave solutions and uncountably infinite many smooth periodic wave solutions is shown. Explicit exact parametric representations for solutions of kink wave, periodic wave and unbounded traveling wave are obtained. 展开更多
关键词 kink wave solution periodic wave solution unbounded wave solution nonlinear wave equation dynamical system method
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Exact traveling wave solutions for an integrable nonlinear evolution equation given by M.Wadati
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作者 李继彬 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第4期437-440,共4页
By using the method of dynamical systems, the travelling wave solutions of for an integrable nonlinear evolution equation is studied. Exact explicit parametric representations of kink and anti-kink wave, periodic wave... By using the method of dynamical systems, the travelling wave solutions of for an integrable nonlinear evolution equation is studied. Exact explicit parametric representations of kink and anti-kink wave, periodic wave solutions and uncountably infinite many smooth solitary wave solutions are given. 展开更多
关键词 solitary wave solution periodic wave solution kink and anti-kink wave solutions nonlinear evolution equation
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Travelling wave solutions for a second order wave equation of KdV type
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作者 龙瑶 李继彬 +1 位作者 芮伟国 何斌 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第11期1455-1465,共11页
The theory of planar dynamical systems is used to study the dynamical behaviours of travelling wave solutions of a nonlinear wave equations of KdV type. In different regions of the parametric space, sufficient conditi... The theory of planar dynamical systems is used to study the dynamical behaviours of travelling wave solutions of a nonlinear wave equations of KdV type. In different regions of the parametric space, sufficient conditions to guarantee the existence of solitary wave solutions, periodic wave solutions, kink and anti-kink wave solutions are given. All possible exact explicit parametric representations are obtained for these waves. 展开更多
关键词 solitary wave solution periodic wave solution kink wave and anti-kin kwave solutions smooth and non-smooth periodic waves
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Bifurcations of traveling wave solutions and exact solutions to generalized Zakharov equation and Ginzburg-Landau equation
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作者 戴振祥 徐园芬 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第12期1615-1622,共8页
This paper studies the dynamic behaviors of some exact traveling wave solutions to the generalized Zakharov equation and the Ginzburg-Landau equation. The effects of the behaviors on the parameters of the systems are ... This paper studies the dynamic behaviors of some exact traveling wave solutions to the generalized Zakharov equation and the Ginzburg-Landau equation. The effects of the behaviors on the parameters of the systems are also studied by using a dynamical system method. Six exact explicit parametric representations of the traveling wave solutions to the two equations are given. 展开更多
关键词 planar dynamical system periodic wave solution nonlinear wave equation
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Bifurcations of travelling wave solutions for Jaulent-Miodek equations
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作者 冯大河 李继彬 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第8期999-1005,共7页
By using the theory of bifurcations of planar dynamic systems to the coupled Jaulent-Miodek equations, the existence of smooth solitary travelling wave solutions and uncountably infinite many smooth periodic travellin... By using the theory of bifurcations of planar dynamic systems to the coupled Jaulent-Miodek equations, the existence of smooth solitary travelling wave solutions and uncountably infinite many smooth periodic travelling wave solutions is studied and the bifurcation parametric sets are shown. Under the given parametric conditions, all possible representations of explicit exact solitary wave solutions and periodic wave solutions are obtained. 展开更多
关键词 Jaulent-Miodek equations solitary wave periodic travelling wave solution
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Dynamical behavior of traveling wave solutions of ion acoustic plasma equations
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作者 李庶民 贺天兰 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第1期119-124,共6页
By using the theory of planar dynamical systems to the ion acoustic plasma equations, we obtain the existence of the solutions of the smooth and non-smooth solitary waves and the uncountably infinite smooth and non-sm... By using the theory of planar dynamical systems to the ion acoustic plasma equations, we obtain the existence of the solutions of the smooth and non-smooth solitary waves and the uncountably infinite smooth and non-smooth periodic waves. Under the given parametric conditions, we present the sufficient conditions to guarantee the existence of the above solutions. 展开更多
关键词 solitary traveling wave solution periodic traveling wave solution smoothness of waves ion acoustic plasma equations
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Using a New Auxiliary Equation to Construct Abundant Solutions for Nonlinear Evolution Equations 被引量:1
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作者 Yifan Liu Guojiang Wu 《Journal of Applied Mathematics and Physics》 2021年第12期3155-3164,共10页
In this paper, a new auxiliary equation method is proposed. Combined with the mapping method, abundant periodic wave solutions for generalized Klein-Gordon equation and Benjamin equation are obtained. They are new typ... In this paper, a new auxiliary equation method is proposed. Combined with the mapping method, abundant periodic wave solutions for generalized Klein-Gordon equation and Benjamin equation are obtained. They are new types of periodic wave solutions which are rarely found in previous studies. As <em>m</em> → 0 and <em>m</em> → 1, some new types of trigonometric solutions and solitary solutions are also obtained correspondingly. This method is promising for constructing abundant periodic wave solutions and solitary solutions of nonlinear evolution equations (NLEEs) in mathematical physics. 展开更多
关键词 Auxiliary Equation Method Nonlinear Evolution Equations periodic wave solutions Mapping Method Solitary wave solutions
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EXPLICIT EXACT SOLUTIONS FOR THE GENERALIZED COMBINED KdV AND MKdV EQUATION
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作者 Yan Zhenya Zhang HongqingDept.ofAppl.Math.,DalianUniv.ofTechnology,Dalian116024 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2001年第2期156-160,共5页
With the aid of Mathematica and Wu elimination method,via using a new generalized ansatz and well known Riccati equation,thirty two families of explicit and exact solutions for the generalized combined KdV and mKdV... With the aid of Mathematica and Wu elimination method,via using a new generalized ansatz and well known Riccati equation,thirty two families of explicit and exact solutions for the generalized combined KdV and mKdV equation are obtained,which contain new solitary wave solutions and periodic wave solutions.This approach can also be applied to other nonlinear evolution equations. 展开更多
关键词 combined KdV and mKdV equation solitary wave solution periodic wave solution.
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New Solutions for an Elliptic Equation Method and Its Applications in Nonlinear Evolution Equations
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作者 Minghuan Liu Yuanguang Zheng 《Journal of Applied Mathematics and Physics》 2022年第8期2415-2431,共17页
In this paper, we study an elliptic equation with four distinct real roots and obtain five new solutions to this type of elliptic equation. Using these obtained new elliptic function solutions we can construct a serie... In this paper, we study an elliptic equation with four distinct real roots and obtain five new solutions to this type of elliptic equation. Using these obtained new elliptic function solutions we can construct a series of explicit exact solutions for many nonlinear evolution equations. As examples, we choose combined KdV-MKdV equation, a fourth-order integrable nonlinear Schr&#246;dinger equation and generalized Dullin-Gottwald-Holm equation to demonstrate the effectiveness of these new elliptic function solutions. These new elliptic function solutions can be applied to many other nonlinear evolution equations. 展开更多
关键词 Elliptic Equation periodic wave solution Singular wave solution Combined KdV-MKdV Equation Generalized Dullin-Gottwald-Holm Equation
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Periodic Wave Solutions and Their Limits for the Modified Kd V–KP Equations 被引量:3
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作者 Ming SONG Zheng Rong LIU Chen Xi YANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2015年第6期1043-1056,共14页
In this paper, we use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the modified KdV-KP equations. Some explicit periodic wave solutions are obtained. These solu... In this paper, we use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the modified KdV-KP equations. Some explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain solitary wave solutions, periodic wave solutions, kink wave solutions and unbounded solutions. 展开更多
关键词 Bifurcation method modified KdV-KP equation periodic wave solutions limits
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The Explicit Periodic Wave Solutions and Their Limit Forms for a Generalized b-equation 被引量:2
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作者 Yi-ren CHEN Wei-bo YE Rui LIU 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2016年第2期513-528,共16页
In this paper, for b ∈ (-∞,∞) and b ≠ -1, -2, we investigate the explicit periodic wave solutions for the generalized b-equation ut + 2kux - uxxt + (1 + b)u2ux =buxuxx + uuxxx, which contains the generaliz... In this paper, for b ∈ (-∞,∞) and b ≠ -1, -2, we investigate the explicit periodic wave solutions for the generalized b-equation ut + 2kux - uxxt + (1 + b)u2ux =buxuxx + uuxxx, which contains the generalized Camassa-Holm equation and the generalized Degasperis-Procesi equation. Firstly, via the methods of dynamical system and elliptic integral we obtain two types of explicit periodic wave solutions with a parametric variable a. One of them is made of two elliptic smooth periodic wave solutions. The other is composed of four elliptic periodic blow-up solutions. Secondly we show that there exist four special values for a. When a tends to these special values, these above solutions have limits. From the limit forms we get other three types of nonlinear wave solutions, hyperbolic smooth solitary wave solution, hyperbolic single blow-up solution, trigonometric periodic blow-up solution. Some previous results are extended. For b = -1 or b = -2, we guess that the equation does not have any one of above solutions. 展开更多
关键词 generalized b-equation elliptic integral method explicit periodic wave solutions limit formes
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Solitons and Bifurcations for the Generalized Tzitzéica Type Equation in Nonlinear Fiber Optics
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作者 Xujie Jiang 《Journal of Applied Mathematics and Physics》 2023年第10期3042-3060,共19页
Solitons and bifurcations for the generalized Tzitzéica type equation are studied by using the theory of dynamical systems and Hamilton function. With the help of Maple and bifurcation theory of differential equa... Solitons and bifurcations for the generalized Tzitzéica type equation are studied by using the theory of dynamical systems and Hamilton function. With the help of Maple and bifurcation theory of differential equations, the bifurcation parameter conditions and all the bifurcation phase portraits are obtained. Because the same energy value of the Hamiltonian function is corresponding to the same orbit, thus the periodic wave solutions, bright soliton and dark soliton solutions are defined. 展开更多
关键词 Generalized Tzitzéica Type Equation Homoclinic Orbit periodic wave solution Bright Soliton Dark Soliton
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