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A Family of the Inertial Manifolds for a Class of Generalized Kirchhoff-Type Coupled Equations
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作者 Guoguang Lin Jiaying Zhou 《Open Journal of Applied Sciences》 CAS 2022年第7期1116-1127,共12页
The paper considers the long-time behavior for a class of generalized high-order Kirchhoff-type coupled equations, under the corresponding hypothetical conditions, according to the Hadamard graph transformation method... The paper considers the long-time behavior for a class of generalized high-order Kirchhoff-type coupled equations, under the corresponding hypothetical conditions, according to the Hadamard graph transformation method, obtain the equivalent norm in space , and we obtain the existence of a family of the inertial manifolds while such equations satisfy the spectral interval condition. 展开更多
关键词 Kirchhoff-Type coupled equations Spectral Interval Condition A Family of the Inertial Manifolds
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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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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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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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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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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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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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Numerical Solutions of a New Type of Fractional Coupled Nonlinear Equations
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作者 CHEN Yong AN Hong-Li 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第4期839-844,共6页
In this paper, we investigate a new type of fractional coupled nonlinear equations. By introducing the fractional derivative that satisfies the Caputo's definition, we directly extend the applications of the Adomian ... In this paper, we investigate a new type of fractional coupled nonlinear equations. By introducing the fractional derivative that satisfies the Caputo's definition, we directly extend the applications of the Adomian decomposition method to the new system. As a result, with the aid of Maple, the realistic and convergent rapidly series solutions are obtained with easily computable components. Two famous fractional coupled examples: KdV and mKdV equations, are used to illustrate the efficiency and accuracy of the proposed method. 展开更多
关键词 Adomian decomposition method fractional calculus fractional coupled equations numerical solution
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New Rational Form Solutions to Coupled Nonlinear Wave Equations
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作者 FU Zun-Tao LIN Guang-Xing +1 位作者 LIU Shi-Kuo LIU Shi-Da 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第2X期235-242,共8页
The new rational form solutions to the elliptic equation are shown, and then these solutions to the elliptic equation are taken as a transformation and applied to solve nonlinear coupled wave equations. It is shown th... The new rational form solutions to the elliptic equation are shown, and then these solutions to the elliptic equation are taken as a transformation and applied to solve nonlinear coupled wave equations. It is shown that more novel kinds of solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form,and so on. 展开更多
关键词 elliptic equation Jacobi elliptic function nonlinear coupled equations periodic wave solution rational form
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Envelope Periodic Solutions to Coupled Nonlinear Equations
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作者 LIUShi-Da FuZun-Tao 《Communications in Theoretical Physics》 SCIE CAS CSCD 2003年第2期167-172,共6页
The envelope periodic solutions to some nonlinear coupled equations are obtained by means of the Jacobielliptic function expansion method. And these envelope periodic solutions obtained by this method can degenerate t... The envelope periodic solutions to some nonlinear coupled equations are obtained by means of the Jacobielliptic function expansion method. And these envelope periodic solutions obtained by this method can degenerate tothe envelope shock wave solutions and/or the envelope solitary wave solutions. 展开更多
关键词 Jacobi elliptic function nonlinear coupled equations envelope periodic solution
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Application of coupled equation method on resonance processes of atomic lithium
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作者 房增科 马晓光 《Chinese Optics Letters》 SCIE EI CAS CSCD 2007年第11期621-623,共3页
The coupled equation method (CEM) has been applied to investigating the resonance structures for the ground state 1s^22s^ 2S of the neutral lithium from the first threshold up to 64.5 eV. Resonance structures of ato... The coupled equation method (CEM) has been applied to investigating the resonance structures for the ground state 1s^22s^ 2S of the neutral lithium from the first threshold up to 64.5 eV. Resonance structures of atomic lithium due to single excitations of the ls and 2s electrons are studied by infinite-order calculations in detail. The effect of spin-orbit splitting is also included for some of the low-lying ls2snp(↑↓) resonance, and the influence of the interference between 1s^2s^3 Snp .↓ and 1s2s^ 1 Snp ↑ states on the resonance structure has been confirmed theoretically. The results show that the presented technique can give the reasonable resonance structures very well in photoionization processes. 展开更多
关键词 Application of coupled equation method on resonance processes of atomic lithium
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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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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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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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On Coupled KdV Equations with Self-consistent Sources 被引量:2
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作者 HUANG Ye-Hui WU Hong-Xia +1 位作者 XIE Xi ZENG Yun-Bo 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第5期1091-1100,共10页
The coupled Korteweg-de Vries (CKdV) equation with self-consistent sources (CKdVESCS) and its Lax representation are derived. We present a generalized binary Darboux transformation (GBDT) with an arbitrary time-... The coupled Korteweg-de Vries (CKdV) equation with self-consistent sources (CKdVESCS) and its Lax representation are derived. We present a generalized binary Darboux transformation (GBDT) with an arbitrary time- dependent function for the CKdVESCS as well as the formula for the N-times repeated GBDT. This GBDT provides non-auto-Biicklund transformation between two CKdVESCSs with different degrees of sources and enables us to construct more generM solutions with N arbitrary t-dependent functions. We obtain positon, negaton, complexiton, and negaton- positon solutions of the CKdVESCS. 展开更多
关键词 coupled KdV equation with self-consistent sources generalized binary Darboux transformation POSITON NEGATON COMPLEXITON
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Nonequivalent Similarity Reductions and Exact Solutions for Coupled Burgers-Type Equations 被引量:2
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作者 M.H.M.Moussa R.A.K.Omar +1 位作者 Rehab M.El-Shiekh H.R.El-Melegy 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第1期1-4,共4页
Using the machinery of Lie group analysis,the nonlinear system of coupled Burgers-type equations is studied.Using the infinitesimal generators in the optimal system of subalgebra of the said Lie algebras,it leads to t... Using the machinery of Lie group analysis,the nonlinear system of coupled Burgers-type equations is studied.Using the infinitesimal generators in the optimal system of subalgebra of the said Lie algebras,it leads to two nonequivalent similarity transformations by using it we obtain two reductions in the form of system of nonlinear ordinary differential equations.The search for solutions of these systems by using the G'/G-method has yielded certain exact solutions expressed by rational functions,hyperbolic functions,and trigonometric functions.Some figures are given to show the properties of the solutions. 展开更多
关键词 symmetry method G/G-method coupled Burgers-type equations exact solutions
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A Coupled Variable Coefficient Modified KdV Equation Arising from a Two-Layer Fluid System 被引量:3
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作者 GAO Yuan~1 and TANG Xiao-Yan~(1,2)~1 Department of Physics,Shanghai Jiao Tong University,Shanghai 200240,China~2 Institut Für Theoretische Physik IV,Fakultt für Physik und Astronomie,Ruhr-Universitt Bochum,D-44870 Bochum,Germany 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第12期961-970,共10页
A quite general coupled variable coefficient modified KdV (VCmKdV) equation in a two-layer fluid systemis derived by means of the reductive perturbation method.Making use of the CK's direct method,some similarityr... A quite general coupled variable coefficient modified KdV (VCmKdV) equation in a two-layer fluid systemis derived by means of the reductive perturbation method.Making use of the CK's direct method,some similarityreductions of the coupled VCmKdV equation are obtained and their corresponding group explanations are discussed.Some exact solutions of the coupled equations are also presented. 展开更多
关键词 coupled variable coefficient mKdV equation two-layer fluid similarity solution periodic waves
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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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Coupled Nonlinear Schrodinger Equation: Symmetries and Exact Solutions 被引量:2
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作者 LIU Ping LOU Sen-Yue 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第1期27-34,共8页
The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger (CNLS) equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie gr... The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger (CNLS) equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries. 展开更多
关键词 coupled nonlinear SchrSdinger equation classical Lie group approach symmetry exact solution
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Soliton Solutions to the Coupled Gerdjikov-Ivanov Equation with Rogue-Wave-Like Phenomena 被引量:2
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作者 Jian-Bing Zhang Ying-Yin Gongye Shou-Ting Chen 《Chinese Physics Letters》 SCIE CAS CSCD 2017年第9期3-7,共5页
Bilinear forms of the coupled Gerdjikov–Ivanov equation are derived. The $N$-soliton solutions to the equation are obtained by Hirota's method. It is interesting that the two-soliton solutions can generate the rogue... Bilinear forms of the coupled Gerdjikov–Ivanov equation are derived. The $N$-soliton solutions to the equation are obtained by Hirota's method. It is interesting that the two-soliton solutions can generate the rogue-wave-like phenomena by selecting special parameters. The equation can be reduced to the Gerdjikov–Ivanov equation as well as its bilinear forms and its solutions. 展开更多
关键词 exp Soliton Solutions to the coupled Gerdjikov-Ivanov equation with Rogue-Wave-Like Phenomena GI
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