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Multi-soliton solutions of coupled Lakshmanan-Porsezian-Daniel equations with variable coefficients under nonzero boundary conditions
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作者 赵会超 马雷诺 解西阳 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第8期137-152,共16页
This paper aims to investigate the multi-soliton solutions of the coupled Lakshmanan–Porsezian–Daniel equations with variable coefficients under nonzero boundary conditions.These equations are utilized to model the ... This paper aims to investigate the multi-soliton solutions of the coupled Lakshmanan–Porsezian–Daniel equations with variable coefficients under nonzero boundary conditions.These equations are utilized to model the phenomenon of nonlinear waves propagating simultaneously in non-uniform optical fibers.By analyzing the Lax pair and the Riemann–Hilbert problem,we aim to provide a comprehensive understanding of the dynamics and interactions of solitons of this system.Furthermore,we study the impacts of group velocity dispersion or the fourth-order dispersion on soliton behaviors.Through appropriate parameter selections,we observe various nonlinear phenomena,including the disappearance of solitons after interaction and their transformation into breather-like solitons,as well as the propagation of breathers with variable periodicity and interactions between solitons with variable periodicities. 展开更多
关键词 soliton Riemann-Hilbert problem non-zero boundary conditions coupled Lakshmanan-Porsezian-Daniel equation
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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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Breather and its interaction with rogue wave of the coupled modified nonlinear Schrodinger equation
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作者 王明 徐涛 +1 位作者 何国亮 田雨 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第5期350-356,共7页
We investigate the coupled modified nonlinear Schr?dinger equation.Breather solutions are constructed through the traditional Darboux transformation with nonzero plane-wave solutions.To obtain the higher-order localiz... We investigate the coupled modified nonlinear Schr?dinger equation.Breather solutions are constructed through the traditional Darboux transformation with nonzero plane-wave solutions.To obtain the higher-order localized wave solution,the N-fold generalized Darboux transformation is given.Under the condition that the characteristic equation admits a double-root,we present the expression of the first-order interactional solution.Then we graphically analyze the dynamics of the breather and rogue wave.Due to the simultaneous existence of nonlinear and self-steepening terms in the equation,different profiles in two components for the breathers are presented. 展开更多
关键词 coupled modified nonlinear Schr?dinger equation Darboux transformation BREATHER rouge wave
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Diverse soliton solutions and dynamical analysis of the discrete coupled mKdV equation with 4×4 Lax pair
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作者 刘雪珂 闻小永 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第12期179-191,共13页
Under consideration in this study is the discrete coupled modified Korteweg-de Vries(mKdV)equation with 4×4 Lax pair.Firstly,through using continuous limit technique,this discrete equation can be mapped to the co... Under consideration in this study is the discrete coupled modified Korteweg-de Vries(mKdV)equation with 4×4 Lax pair.Firstly,through using continuous limit technique,this discrete equation can be mapped to the coupled KdV and mKdV equations,which may depict the development of shallow water waves,the optical soliton propagation in cubic nonlinear media and the Alfven wave in a cold collision-free plasma.Secondly,the discrete generalized(r,N-r)-fold Darboux transformation is constructed and extended to solve this discrete coupled equation with the fourth-order linear spectral problem,from which diverse exact solutions including usual multi-soliton and semi-rational soliton solutions on the vanishing background,higher-order rational soliton and mixed hyperbolic-rational soliton solutions on the non-vanishing background are derived,and the limit states of some soliton and rational soliton solutions are analyzed by the asymptotic analysis technique.Finally,the numerical simulations are used to explore the dynamical behaviors of some exact soliton solutions.These results may be helpful for understanding some physical phenomena in fields of shallow water wave,optics,and plasma physics. 展开更多
关键词 discrete coupled mKdV equation continuous limit discrete generalized(r N-r)-fold Darboux transformation multi-soliton solutions rational soliton solutions
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An Extension of Mapping Deformation Method and New Exact Solution for Three Coupled Nonlinear Partial Differential Equations 被引量:11
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作者 LIHua-Mei 《Communications in Theoretical Physics》 SCIE CAS CSCD 2003年第4期395-400,共6页
In this paper, we extend the mapping deformation method proposed by Lou. It is used to find new exacttravelling wave solutions of nonlinear partial differential equation or coupled nonlinear partial differential equat... In this paper, we extend the mapping deformation method proposed by Lou. It is used to find new exacttravelling wave solutions of nonlinear partial differential equation or coupled nonlinear partial differential equations(PDEs). Based on the idea of the homogeneous balance method, we construct the general mapping relation betweenthe solutions of the PDEs and those of the cubic nonlinear Klein-Gordon (NKG) equation. By using this relation andthe abundant solutions of the cubic NKG equation, many explicit and exact travelling wave solutions of three systemsof coupled PDEs, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic functionsolutions, and rational solutions, are obtained. 展开更多
关键词 coupled nonlinear partial differential equations cubic nonlinear Klein-Gordon equation exact solution
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Cyclic constitutive equations of rock with coupled damage induced by compaction and cracking 被引量:6
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作者 Chonghong Ren Jin Yu +2 位作者 Xueying Liu Zhuqing Zhang Yanyan Cai 《International Journal of Mining Science and Technology》 SCIE EI CAS CSCD 2022年第5期1153-1165,共13页
In this paper,the cyclic constitutive equations were proposed to describe the constitutive behavior of cyclic loading and unloading.Firstly,a coupled damage variable was derived,which contains two parts,i.e.,the compa... In this paper,the cyclic constitutive equations were proposed to describe the constitutive behavior of cyclic loading and unloading.Firstly,a coupled damage variable was derived,which contains two parts,i.e.,the compaction-induced damage and the cracking-induced damage.The compaction-induced damage variable was derived from a nonlinear stress–strain relation of the initial compaction stage,and the cracking-induced damage variable was established based on the statistical damage theory.Secondly,based on the total damage variable,a damage constitutive equation was proposed to describe the constitutive relation of rock under the monotonic uniaxial compression conditions,whereafter,the application of this model is extended to cyclic loading and unloading conditions.To validate the proposed monotonic and cyclic constitutive equations,a series of mechanical tests for marble specimens were carried out,which contained the monotonic uniaxial compression(MUC)experiment,cyclic uniaxial compression experiments under the variable amplitude(CUC-VA)and constant amplitude(CUC-CA)conditions.The results show that the proposed total damage variable comprehensively reflects the damage evolution characteristic,i.e.,the damage variable firstly decreases,then increases no matter under the conditions of MUC,CUC-VA or CUC-CA.Then a reasonable consistency is observed between the experimental and theoretical curves.The proposed cyclic constitutive equations can simulate the whole cyclic loading and unloading behaviors,such as the initial compaction,the strain hardening and the strain softening.Furthermore,the shapes of the theoretical curves are controlled by the modified coefficient,compaction sensitivity coefficient and two Weibull distributed parameters. 展开更多
关键词 Cyclic constitutive equations ROCK coupled damage COMPACTION CRACKING
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Average vector field methods for the coupled Schrdinger KdV equations 被引量:3
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作者 张弘 宋松和 +1 位作者 陈绪栋 周炜恩 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第7期242-250,共9页
The energy preserving average vector field (AVF) method is applied to the coupled Schr6dinger-KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction di... The energy preserving average vector field (AVF) method is applied to the coupled Schr6dinger-KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction discretization. In order to accelerate our simulation, the split-step technique is used. The numerical experiments show that the non-splitting scheme and splitting scheme are both effective, and have excellent long time numerical behavior. The comparisons show that the splitting scheme is faster than the non-splitting scheme, but it is not as good as the non-splitting scheme in preserving the invariants. 展开更多
关键词 coupled Schrodinger-KdV equations average vector field method splitting method Fourier pseu-dospectral method
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Local discontinuous Galerkin method for solving Burgers and coupled Burgers equations 被引量:2
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作者 张荣培 蔚喜军 赵国忠 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第11期41-46,共6页
In the current work, we extend the local discontinuous Galerkin method to a more general application system. The Burgers and coupled Burgers equations are solved by the local discontinuous Galerkin method. Numerical e... In the current work, we extend the local discontinuous Galerkin method to a more general application system. The Burgers and coupled Burgers equations are solved by the local discontinuous Galerkin method. Numerical experiments are given to verify the efficiency and accuracy of our method. Moreover the numerical results show that the method can approximate sharp fronts accurately with minimal oscillation. 展开更多
关键词 local discontinuous Galerkin method Burgers equation coupled Burgers equation
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Multi-soliton solutions for the coupled modified nonlinear Schrdinger equations via Riemann–Hilbert approach 被引量:3
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作者 Zhou-Zheng Kang Tie-Cheng Xia Xi Ma 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第7期171-178,共8页
The coupled modified nonlinear Schrodinger equations are under investigation in this work. Starting from analyzing the spectral problem of the Lax pair, a Riemann-Hilbert problem for the coupled modified nonlinear Sch... The coupled modified nonlinear Schrodinger equations are under investigation in this work. Starting from analyzing the spectral problem of the Lax pair, a Riemann-Hilbert problem for the coupled modified nonlinear Schrodinger equations is formulated. And then, through solving the obtained Riemann-Hilbert problem under the conditions of irregularity and reflectionless case, N-soliton solutions for the equations are presented. Furthermore, the localized structures and dynamic behaviors of the one-soliton solution are shown graphically. 展开更多
关键词 coupled modified nonlinear Schrodinger equations Riemann-Hilbert approach multi-soliton so-lutions
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Asymptotical solutions of coupled nonlinear Schrodinger equations with perturbations 被引量:2
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作者 程雪苹 林机 叶丽军 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第9期2503-2509,共7页
In this paper Lou's direct perturbation method is applied to the perturbed coupled nonlinear Schrodinger equations to obtain their asymptotical solutions, which include not only the zero-order solutions but also the ... In this paper Lou's direct perturbation method is applied to the perturbed coupled nonlinear Schrodinger equations to obtain their asymptotical solutions, which include not only the zero-order solutions but also the first-order modifications. Based on the asymptotical solutions, the effects of perturbations on soliton parameters and the collision between two solitons are then discussed in brief. Furthermore, we directly simulate the perturbed coupled nonlinear SchrSdinger equations by split-step Fourier method to check the validity of the direct perturbation method. It turns out that our analytical results are well supported by the numerical calculations. 展开更多
关键词 direct perturbation method perturbed coupled nonlinear Schrodinger equations soli- tons asymptotical solutions
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Hausdorff Dimension and Fractal Dimension of the Global Attractor for the Higher-Order Coupled Kirchhoff-Type Equations 被引量:4
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作者 Guoguang Lin Sanmei Yang 《Journal of Applied Mathematics and Physics》 2017年第12期2411-2424,共14页
This paper mainly deals with the higher-order coupled Kirchhoff-type equations with nonlinear strong damped and source terms in a bounded domain. We obtain some results that are estimation of the upper bounds of Hausd... This paper mainly deals with the higher-order coupled Kirchhoff-type equations with nonlinear strong damped and source terms in a bounded domain. We obtain some results that are estimation of the upper bounds of Hausdorff dimension and Fractal dimension of the global attractor. 展开更多
关键词 HIGHER-ORDER coupled Kirchhoff-Type equations Source Term Hausdorff DIMENSION Fractal DIMENSION Nonlinear Dissipation
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On Reduced Variational Equations of Coupled Systems 被引量:3
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作者 Zeng Xianwu Du Nailin Chen Shihua 《Wuhan University Journal of Natural Sciences》 CAS 1997年第2期21-25,共5页
A coupled system of three nonlinear oscillators with symmetric couplings is studied.It turns out that there exists a reduced variational equation to the in phase periodic solution of such a coupled system.By the symme... A coupled system of three nonlinear oscillators with symmetric couplings is studied.It turns out that there exists a reduced variational equation to the in phase periodic solution of such a coupled system.By the symmetry one establishes a structural property for the monodromy matrix of the reduced variational equation,which simplifies the computation of multipliers to a great extent.As an application of the above results,a coupled system of three Poincare oscillators is discussed as well. 展开更多
关键词 coupled system reduced variational equation STABILITY
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The Inertial Manifolds for a Class of Higher-Order Coupled Kirchhoff-Type Equations 被引量:3
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作者 Guoguang Lin Sanmei Yang 《Journal of Applied Mathematics and Physics》 2018年第5期1055-1064,共10页
In this paper, we mainly deal with a class of higher-order coupled Kirch-hoff-type equations. At first, we take advantage of Hadamard’s graph to get the equivalent form of the original equations. Then, the inertial m... In this paper, we mainly deal with a class of higher-order coupled Kirch-hoff-type equations. At first, we take advantage of Hadamard’s graph to get the equivalent form of the original equations. Then, the inertial manifolds are proved by using spectral gap condition. The main result we gained is that the inertial manifolds are established under the proper assumptions of M(s) and gi(u,v), i=1, 2. 展开更多
关键词 HIGHER-ORDER coupled Kirchhoff-Type equations Inertial MANIFOLD Hadamard’s Graph Spectral Gap Condition
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Two-Soliton Solutions and Interactions for the Generalized Complex Coupled Kortweg-de Vries Equations 被引量:2
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作者 GAI Xiao-Ling GAO Yi-Tian +2 位作者 YU Xin SUN Zhi-Yuan WANG Lei 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第3期473-480,共8页
Kortweg-de Vries (KdV)-typed equations have been used to describe certain nonlinear phenomena in fluids and plasmas. Generalized complex coupled KdV (GCCKdV) equations are investigated in this paper. Through the d... Kortweg-de Vries (KdV)-typed equations have been used to describe certain nonlinear phenomena in fluids and plasmas. Generalized complex coupled KdV (GCCKdV) equations are investigated in this paper. Through the dependent variable transformations and symbolic computation, GCCKdV equations are transformed into their bilinear forms, based on which the one- and two-soliton solutions are obtained. Through the interactions of two solitons, the regular elastic collision are shown. When the wave numbers are complex, three kinds of solitonie collisions are presented: (i) two solitons merge and separate from each other periodically; (ii) two solitons exhibit the attraction and repulsion nearly twice, and finally separate from each other after such type of interaction; (iii) two solitons are ftuctuant in the central region of the collision. Propagation features of solitons are investigated with the effects of the coefficients in the GCCKdV equations considered. Velocity of soliton increase with the a increasing. Amplitude of v increase with the a increasing and decrease with the β increasing. 展开更多
关键词 generalized complex coupled KdV equations bilinear equations two-soliton solutions INTERACTIONS symbolic computation
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New finite-gap solutions for the coupled Burgers equations engendered by the Neumann systems 被引量:1
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作者 陈金兵 耿献国 乔志军 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第9期202-211,共10页
On the tangent bundle TSN-1 of the unit sphere SN-l, this paper reduces the coupled Burgers equations to two Neumann systems by using the nonlinearization of the Lax pair, whose Liouville integrability is displayed in... On the tangent bundle TSN-1 of the unit sphere SN-l, this paper reduces the coupled Burgers equations to two Neumann systems by using the nonlinearization of the Lax pair, whose Liouville integrability is displayed in the scheme of the r-matrix technique. Based on the Lax matrix of the Neumann systems, the Abel-Jacobi coordinates are appropriately chosen to straighten out the restricted Neumann flows on the complex torus, from which the new finite-gap solutions expressed by Riemann theta functions for the coupled Burgers equations are given in view of the Jacobi inversion. 展开更多
关键词 coupled Burgers equations Lax matrix Jacobi inversion finite-gap solutions
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Exact solutions for four coupled complex nonlinear differential equations 被引量:1
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作者 胡建兰 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第11期3192-3196,共5页
In this paper, exact solutions are derived for four coupled complex nonlinear different equations by using simplified transformation method and algebraic equations.
关键词 exact solutions complex coupled equations transformation method
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Boundary-layer eigen solutions for multi-field coupled equations in the contact interface 被引量:1
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作者 侯磊 李涵灵 +2 位作者 张家健 林德志 仇磷 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第6期719-732,共14页
The dissipative equilibrium dynamics studies the law of fluid motion under constraints in the contact interface of the coupling system. It needs to examine how con- straints act upon the fluid movement, while the flui... The dissipative equilibrium dynamics studies the law of fluid motion under constraints in the contact interface of the coupling system. It needs to examine how con- straints act upon the fluid movement, while the fluid movement reacts to the constraint field. It also needs to examine the coupling fluid field and media within the contact in- terface, and to use the multi-scale analysis to solve the regular and singular perturbation problems in micro-phenomena of laboratories and macro-phenomena of nature. This pa- per describes the field affected by the gravity constraints. Applying the multi-scale anal- ysis to the complex Fourier harmonic analysis, scale changes, and the introduction of new parameters, the complex three-dimensional coupling dynamic equations are transformed into a boundary layer problem in the one-dimensional complex space. Asymptotic analy- sis is carried out for inter and outer solutions to the perturbation characteristic function of the boundary layer equations in multi-field coupling. Examples are given for disturbance analysis in the flow field, showing the turning point from the index oscillation solution to the algebraic solution. With further analysis and calculation on nonlinear eigenfunctions of the contact interface dynamic problems by the eigenvalue relation, an asymptotic per- turbation solution is obtained. Finally, a boundary layer solution to multi-field coupling problems in the contact interface is obtained by asymptotic estimates of eigenvalues for the G-N mode in the large flow limit. Characteristic parameters in the final form of the eigenvalue relation are key factors of the dissipative dynamics in the contact interface. 展开更多
关键词 coupling dynamic equations boundary problem EIGENVALUE asymptotic perturbation analysis turning point
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Exact solutions for the coupled Klein-Gordon-Schrǒdinger equations using the extended F-expansion method 被引量:1
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作者 何红生 陈江 杨孔庆 《Chinese Physics B》 SCIE EI CAS CSCD 2005年第10期1926-1931,共6页
The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations (K-G-S equations) by the aid of the symbolic computation system Mathematica. ... The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations (K-G-S equations) by the aid of the symbolic computation system Mathematica. More solutions in the Jacobi elliptic function form are obtained, including the single Jacobi elliptic function solutions, combined Jacobi elliptic function solutions, rational solutions, triangular solutions, soliton solutions and combined soliton solutions. 展开更多
关键词 extended F-expansion method exact solutions coupled K-G-S equations Jacobi elliptic function
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The periodic solutions for coupled integrable dispersionless equations 被引量:1
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作者 刘式适 赵强 刘式达 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第4期5-7,共3页
By using the Jacobi elliptic-function method, this paper obtains the periodic solutions for coupled integrable dispersionless equations. The periodic solutions include some kink and anti-kink solitons.
关键词 periodic solutions coupled integrable dispersionless equations Jacobi elliptic-function method
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Exact periodic solution in coupled nonlinear Schodinger equations 被引量:1
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作者 李齐良 陈均朗 +1 位作者 余淑毅 钱胜 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第6期1545-1548,共4页
The coupled nonlinear Schodinger equations (CNLSEs) of two symmetrical optical fibres are nonintegrable, however the transformed CNLSEs have integrability. Integrability of the transformed CNLSEs is proved by the Ha... The coupled nonlinear Schodinger equations (CNLSEs) of two symmetrical optical fibres are nonintegrable, however the transformed CNLSEs have integrability. Integrability of the transformed CNLSEs is proved by the Hamilton dynamics theory and Galilei transform. Making use of a transform for CNLSEs and using the ansatz with Jacobi elliptic function form, this paper obtains the exact optical pulse solutions. 展开更多
关键词 dual core fibre the coupled nonlinear SchrSdinger equations elliptic function
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