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Multiple exp-function method for soliton solutions of nonlinear evolution equations
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作者 Yakup Yιldιrιm Emrullah Yasar 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第7期20-26,共7页
We applied the multiple exp-function scheme to the(2+1)-dimensional Sawada-Kotera(SK) equation and(3+1)-dimensional nonlinear evolution equation and analytic particular solutions have been deduced. The analyti... We applied the multiple exp-function scheme to the(2+1)-dimensional Sawada-Kotera(SK) equation and(3+1)-dimensional nonlinear evolution equation and analytic particular solutions have been deduced. The analytic particular solutions contain one-soliton, two-soliton, and three-soliton type solutions. With the assistance of Maple, we demonstrated the efficiency and advantages of the procedure that generalizes Hirota's perturbation scheme. The obtained solutions can be used as a benchmark for numerical solutions and describe the physical phenomena behind the model. 展开更多
关键词 (2+1)-dimensional Sawada-Kotera(SK) equation (3+1)-dimensional nonlinear evolution equation(NLEE) multiple exp-function method multiple wave solutions
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Interaction properties of solitons for a couple of nonlinear evolution equations 被引量:1
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作者 Syed Tahir Raza Rizvi Ishrat Bibi +1 位作者 Muhammad Younis Ahmet Bekir 《Chinese Physics B》 SCIE EI CAS CSCD 2021年第1期185-190,共6页
We study one-and two-soliton solutions for the Cahn–Allen(CA) equation and the Brethorton equation. The CA equation has broad spectrum of applications especially in anti-phase boundary motion and it is used in phase-... We study one-and two-soliton solutions for the Cahn–Allen(CA) equation and the Brethorton equation. The CA equation has broad spectrum of applications especially in anti-phase boundary motion and it is used in phase-field models.While the Brethorton equation is a model for dispersive wave systems, it is used to find the resonant nonlinear interaction among three linear modes. We use the Hirota bilinear method to obtain one-and two-soliton solutions to the CA equation and the Brethorton equation. 展开更多
关键词 Hirota bilinear method soliton interaction evolution equations
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Bright soliton dynamics for resonant nonlinear Schrödinger equation with generalized cubic-quintic nonlinearity
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作者 Keyu Bao Xiaogang Tang Ying Wang 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第12期278-288,共11页
For systems modeled by the resonant nonlinear Schrödinger equation(RNLSE)with generalized cubic-quintic nonlinearity,we derive the bright soliton solution of the equation in(1+1)dimensions,using the modified F-ex... For systems modeled by the resonant nonlinear Schrödinger equation(RNLSE)with generalized cubic-quintic nonlinearity,we derive the bright soliton solution of the equation in(1+1)dimensions,using the modified F-expansion method along with the novel ansatz of F-base function.Furthermore,we extend the analytical study of soliton dynamics to higher(2+1)and(3+1)dimensions by using the self-similar method,and demonstrate the soliton behavior via graphical illustration.Moreover,we investigate the effect of the resonance term on bright soliton solution in(1+1)dimensions.Additionally,we consider the nonlinear equation models with perturbation terms and derive the bright soliton solutions for the one-dimensional(1D)to three-dimensional(3D)cases.The theoretical results derived can be used to guide the experimental studies and observations of bright solitons in systems described by RNLSE model. 展开更多
关键词 soliton resonant nonlinear Schrödinger equation F-expansion method
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A more general form of lump solution,lumpoff,and instanton/rogue wave solutions of a reduced (3+1)-dimensional nonlinear evolution equation 被引量:2
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作者 Panfeng Zheng Man Jia 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第12期147-156,共10页
In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution ... In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution to the special case for z=x.Furthermore,a more general form of lump solution of the equation is found which possesses seven arbitrary parameters and four constraint conditions.By cutting the lump by the induced soliton(s),lumpoff and instanton/rogue wave solutions are also constructed by the more general form of lump solution. 展开更多
关键词 a reduced(3 + 1)-dimensional nonlinear evolution equation more general form of lump solution soliton induced by lump lumpoff and instanton/rogue wave solutions
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Nondegenerate solitons of the(2+1)-dimensional coupled nonlinear Schrodinger equations with variable coefficients in nonlinear optical fibers
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作者 杨薇 程雪苹 +1 位作者 金桂鸣 王佳楠 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第12期170-178,共9页
We derive the multi-hump nondegenerate solitons for the(2+1)-dimensional coupled nonlinear Schrodinger equations with propagation distance dependent diffraction,nonlinearity and gain(loss)using the developing Hirota b... We derive the multi-hump nondegenerate solitons for the(2+1)-dimensional coupled nonlinear Schrodinger equations with propagation distance dependent diffraction,nonlinearity and gain(loss)using the developing Hirota bilinear method,and analyze the dynamical behaviors of these nondegenerate solitons.The results show that the shapes of the nondegenerate solitons are controllable by selecting different wave numbers,varying diffraction and nonlinearity parameters.In addition,when all the variable coefficients are chosen to be constant,the solutions obtained in this study reduce to the shape-preserving nondegenerate solitons.Finally,it is found that the nondegenerate two-soliton solutions can be bounded to form a double-hump two-soliton molecule after making the velocity of one double-hump soliton resonate with that of the other one. 展开更多
关键词 nondegenerate solitons variable coefficients coupled nonlinear Schr?dinger equations Hirota bilinear method
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The homotopic mapping solution for the solitary wave for a generalized nonlinear evolution equation 被引量:21
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作者 莫嘉琪 林苏榕 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第9期3628-3631,共4页
This paper studies a generalized nonlinear evolution equation. Using the homotopic mapping method, it constructs a corresponding homotopic mapping transform. Selecting a suitable initial approximation and using homoto... This paper studies a generalized nonlinear evolution equation. Using the homotopic mapping method, it constructs a corresponding homotopic mapping transform. Selecting a suitable initial approximation and using homotopic mapping, it obtains an approximate solution with an arbitrary degree of accuracy for the solitary wave. From the approximate solution obtained by using the homotopic mapping method, it possesses a good accuracy. 展开更多
关键词 evolution equation nonlinear soliton approximate method
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A new expansion method of first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term and its application to mBBM model 被引量:3
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作者 潘军廷 龚伦训 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第2期399-402,共4页
Based on a first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term which is extended from a type of elliptic equation, and by converting it into a new expansion form, this paper... Based on a first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term which is extended from a type of elliptic equation, and by converting it into a new expansion form, this paper proposes a new algebraic method to construct exact solutions for nonlinear evolution equations. Being concise and straightforward, the method is applied to modified Benjamin-Bona-Mahony (mBBM) model, and some new exact solutions to the system are obtained. The algorithm is of important significance in exploring exact solutions for other nonlinear evolution equations. 展开更多
关键词 nonlinear evolution equations new expansion method mBBM model exact solutions
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Some new solutions derived from the nonlinear (2+1)-dimensional Toda equation-an efficient method of creating solutions 被引量:4
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作者 白成林 张霞 张立华 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第2期475-481,共7页
This paper presents a new and efficient approach for constructing exact solutions to nonlinear differential-difference equations (NLDDEs) and lattice equation. By using this method via symbolic computation system MA... This paper presents a new and efficient approach for constructing exact solutions to nonlinear differential-difference equations (NLDDEs) and lattice equation. By using this method via symbolic computation system MAPLE, we obtained abundant soliton-like and/or period-form solutions to the (2+1)-dimensional Toda equation. It seems that solitary wave solutions are merely special cases in one family. Furthermore, the method can also be applied to other nonlinear differential-difference equations. 展开更多
关键词 hyperbolic function method nonlinear differential-difference equations soliton-like solutions period-form solutions
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Nondegenerate and Degenerate Multi-Solitons for the Reverse-Time Nonlocal Nonlinear Schrodinger Model
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作者 Jin-Hao Liu Kai-Li Geng Chao-Qing Dai 《Chinese Physics Letters》 2025年第4期1-8,共8页
We employ the Hirota bilinear method to systematically derive nondegenerate bright one-and two-soliton solutions,along with degenerate bright-dark two-and four-soliton solutions for the reverse-time nonlocal nonlinear... We employ the Hirota bilinear method to systematically derive nondegenerate bright one-and two-soliton solutions,along with degenerate bright-dark two-and four-soliton solutions for the reverse-time nonlocal nonlinear Schr¨odinger equation.Beyond the fundamental nondegenerate one-soliton solution,we have identified and characterized nondegenerate breather bound state solitons,with particular emphasis on their evolution dynamics. 展开更多
关键词 dark solitons nondegenerate breather bound state solitonswith reverse time nonlocal nonlinear Schr dinger equation nondegenerate solitons bright solitons evolution dynamics degenerate solitons Hirota bilinear method
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Loop Soliton Solutions of a Short Wave Model for a Degasperis-Procesi Equation
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作者 邹丽 宗智 +1 位作者 王振 张朔 《Journal of Marine Science and Application》 2011年第2期220-225,共6页
An analytic method, i.e. the homotopy analysis method, was applied for constructing the solutions of the short waves model equations associated with the Degasperis-Procesi (DP) shallow water waves equation. The explic... An analytic method, i.e. the homotopy analysis method, was applied for constructing the solutions of the short waves model equations associated with the Degasperis-Procesi (DP) shallow water waves equation. The explicit analytic solutions of loop soliton governing the propagation of short waves were obtained. By means of the transformation of independent variables, an analysis one-loop soliton solution expressed by a series of exponential functions was obtained, which agreed well with the exact solution. The results reveal the validity and great potential of the homotopy analysis method in solving complicated solitary water wave problems. 展开更多
关键词 homotopy analysis method one-loop soliton explicit analytic solution nonlinearITY Degasperis-Procesi equation
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On Stability of Full Discrete Nonlinear Gálerkin Method(Dedicated to Professor You Zhaoyong for his 60th brithday) 被引量:1
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作者 Li Kaitai (Institute for Computational & Applied Mathematics, Xi’an Jiaotong University) 《工程数学学报》 CSCD 1991年第2期1-8,共8页
This paper discuss stability of the full discrete nonlinear Galerkin method based on the approximation inertial manifold method for some nonlinear evolution equation, for example, some nonlinear reactor equation and N... This paper discuss stability of the full discrete nonlinear Galerkin method based on the approximation inertial manifold method for some nonlinear evolution equation, for example, some nonlinear reactor equation and Navier-Stokes Equation. In the paper we provide some necessary and sufficient conditions of stability. 展开更多
关键词 Full DISCRETE nonlinear GALERKIN method nonlinear evolution equations STABILITY
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Second-order nonlinear differential operators possessing invariant subspaces of submaximal dimension 被引量:6
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作者 朱春蓉 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第1期42-49,共8页
The invariant subspace method is used to construct the explicit solution of a nonlinear evolution equation. The second-order nonlinear differential operators that possess invariant subspaces of submaximal dimension ar... The invariant subspace method is used to construct the explicit solution of a nonlinear evolution equation. The second-order nonlinear differential operators that possess invariant subspaces of submaximal dimension are described. There are second-order nonlinear differential operators, including cubic operators and quadratic operators, which preserve an invariant subspace of submaximal dimension. A full. description, of the second-order cubic operators with constant coefficients admitting a four-dimensional invariant subspace is given. It is shown that the maximal dimension of invaxiant subspaces preserved by a second-order cubic operator is four. Several examples are given for the construction of the exact solutions to nonlinear evolution equations with cubic nonlinearities. These solutions blow up in a finite 展开更多
关键词 nonlinear evolution equations cubic operators invariant subspace method submaximal dimension blow-up solution
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Third-order nonlinear differential operators preserving invariant subspaces of maximal dimension 被引量:6
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作者 屈改珠 张顺利 李尧龙 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第11期118-124,共7页
In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order qua... In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order quadratic operators with constant coefficients is obtained. One example is given to derive special solutions for evolution equations with third-order quadratic operators. 展开更多
关键词 nonlinear evolution equation quadratic operator invariant subspace method blow-up solution
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Application of Exp-function Method to KdV-Burgers-Kuramoto Equation and Kuramoto-Sivashinsky Equation
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作者 陈博奎 刘伊可 汪秉宏 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第4期562-571,共10页
This paper focuses on the application of Exp-function method to obtain generalized solutions of the KdV-Burgers-Kuramoto equation and the Kuramoto-Sivashinsky equation.It is demonstrated that the Exp-function method p... This paper focuses on the application of Exp-function method to obtain generalized solutions of the KdV-Burgers-Kuramoto equation and the Kuramoto-Sivashinsky equation.It is demonstrated that the Exp-function method provides a mathematical tool for solving the nonlinear evolution equation in mathematical physics. 展开更多
关键词 Exp-function method nonlinear evolution equation KdV-Burgers-Kuramoto equation Kuramoto-Sivashinsky equation
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N-soliton Solution for Two Multidimensional Analogues of the m-KdV Equation
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作者 MA Yun-ling 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第3期434-439,共6页
Using the Hirota's bilinear method,some new N-soliton solution are presented for two multidimensional analogues of the m-KdV equation wt+wxxx-6w 2 wx+3 2( w x -1 wy+w-x -1 wz)x=0 and wt+wxxx?6w 2 wx+3 2( wwy+wx-x-... Using the Hirota's bilinear method,some new N-soliton solution are presented for two multidimensional analogues of the m-KdV equation wt+wxxx-6w 2 wx+3 2( w x -1 wy+w-x -1 wz)x=0 and wt+wxxx?6w 2 wx+3 2( wwy+wx-x-1 wy)=0 in view of a different treatment. 展开更多
关键词 nonlinear evolution equation Hirota’s bilinear method N-soliton solution
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Existence of Formal Conservation Laws of a Variable-Coefficient Korteweg-de Vries Equation from Fluid Dynamics and Plasma Physics via Symbolic Computation 被引量:2
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作者 张春义 李娟 +2 位作者 孟祥花 许韬 高以天 《Chinese Physics Letters》 SCIE CAS CSCD 2008年第3期878-880,共3页
Employing the method which can be used to demonstrate the infinite conservation laws for the standard Kortewegde Vries (KdV) equation, we prove that the variable-coeFficient KdV equation under the Painlevé test... Employing the method which can be used to demonstrate the infinite conservation laws for the standard Kortewegde Vries (KdV) equation, we prove that the variable-coeFficient KdV equation under the Painlevé test condition also possesses the formal conservation laws. 展开更多
关键词 nonlinear evolution-equationS SOLITARY WAVES MATHEMATICAL APPROACH POSITONIC SOLUTIONS KDV equation DUSTY PLASMA MODEL TRANSFORMATION solitonS DEVRIES
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耦合非线性薛定谔方程组孤立子解的局部间断Petrov-Galerkin方法数值模拟
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作者 赵国忠 蔚喜军 《工程数学学报》 CSCD 北大核心 2024年第6期1109-1132,共24页
耦合非线性薛定谔方程组在量子物理、非线性光学、晶体物理、波色–爱因斯坦凝聚和水波动力学等很多物理领域有着重要的应用价值。提出了一种局部间断PetrovGalerkin方法。首先,将耦合非线性薛定谔方程组改写为一阶微分方程组。空间离... 耦合非线性薛定谔方程组在量子物理、非线性光学、晶体物理、波色–爱因斯坦凝聚和水波动力学等很多物理领域有着重要的应用价值。提出了一种局部间断PetrovGalerkin方法。首先,将耦合非线性薛定谔方程组改写为一阶微分方程组。空间离散采用间断Petrov-Galerkin方法,时间离散采用三阶总变差不增Runge-Kutta方法。数值实验表明,该算法对线性元和二次元都能达到最优收敛阶。通过数值算例计算了质量、动量和能量守恒量,该算法可以很好地模拟单孤立子传输、双孤立子碰撞和三孤立子碰撞现象。此外,该算法可以在较长的时间间隔内模拟复杂波型的相互作用或传播,还可以模拟孤子传输和孤子产生现象。 展开更多
关键词 局部间断Petrov-Galerkin方法 耦合非线性薛定谔方程 孤立子碰撞 守恒量
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强非局域介质中高斯型损耗空间光孤子 被引量:7
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作者 王形华 谢应茂 +1 位作者 王磊 吴诗敏 《强激光与粒子束》 EI CAS CSCD 北大核心 2007年第11期1792-1796,共5页
利用变分法研究了1+1维傍轴高斯光束在含有小损耗的强非局域非线性介质中的传输特性,得到了光束各参量的演化方程、束宽的演化规律和一个临界功率。在介质损耗足够小的前提下,当光束初始功率等于临界功率时,得到了一个束宽随传输距离缓... 利用变分法研究了1+1维傍轴高斯光束在含有小损耗的强非局域非线性介质中的传输特性,得到了光束各参量的演化方程、束宽的演化规律和一个临界功率。在介质损耗足够小的前提下,当光束初始功率等于临界功率时,得到了一个束宽随传输距离缓慢展宽的准空间光孤子——损耗空间光孤子;当光束初始功率小于临界功率时,光束束宽则按雅可比椭圆正弦函数和椭圆余弦函数作准周期展宽变化;当光束初始功率大于临界功率时,光束束宽将从按雅可比椭圆正弦函数和椭圆余弦函数作准周期压缩变化过渡到按雅可比椭圆正弦函数和椭圆余弦函数准周期展宽变化。 展开更多
关键词 非线性光学 变分法 强非局域介质 非局域非线性薛定谔方程 小损耗 损耗孤子
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具任意次非线性项的Liénard方程的精确解及其应用 被引量:11
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作者 张卫国 常谦顺 李用声 《数学物理学报(A辑)》 CSCD 北大核心 2005年第1期119-129,共11页
该文推导了具任意次非线性项的Liénard方程a″(ξ)+la(ξ)+maq(ξ)+na2q-1(ξ)=0和a″(ξ)+ra′(ξ)+la(ξ)+maq(ξ)+na2q-1(ξ)=0解的若干性质,通过适当变换,并结合假设待定法求出了它们的钟状和扭状显式精确解.据此,求出了一批... 该文推导了具任意次非线性项的Liénard方程a″(ξ)+la(ξ)+maq(ξ)+na2q-1(ξ)=0和a″(ξ)+ra′(ξ)+la(ξ)+maq(ξ)+na2q-1(ξ)=0解的若干性质,通过适当变换,并结合假设待定法求出了它们的钟状和扭状显式精确解.据此,求出了一批具任意次非线性项的发展方程的钟状和扭状显式精确孤波解,其中包括广义BBM型方程、二维广义Klein-Gordon方程、广义Pochhammer-Chree方程和非线性波方程等. 展开更多
关键词 孤波 LIÉNARD方程 非线性发展方程 精确解 待定假设法
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一类非线性弹性杆波动方程的求解 被引量:5
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作者 郭鹏 张磊 +1 位作者 吕克璞 段文山 《应用数学和力学》 CSCD 北大核心 2008年第1期57-61,共5页
对计入横向惯性效应后的非线性弹性杆纵向波动方程进行了分析,得到了一类非线性波动方程,并用完全近似方法求出了该方程的近似解析解.
关键词 非线性弹性杆 完全近似法 KDV方程 组合KdV方程和mKdV方程
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