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Bifurcations, Analytical and Non-Analytical Traveling Wave Solutions of (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation
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作者 Dahe Feng Jibin Li Airen Zhou 《Applied Mathematics》 2024年第8期543-567,共25页
For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits ... For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation. 展开更多
关键词 (2 + 1)-Dimensional Nonlinear dispersive Boussinesq equation BIFURCATIONS Phase Portrait Analytical Periodic Wave Solution Periodic Cusp Wave Solution
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Selective Impact of Dispersion and Nonlinearity on Waves and Solitary Wave in a Strongly Nonlinear and Flattened Waveguide
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作者 Christian Regis Ngouo Tchinda Marcelle Nina Zambo Abou’ou Jean Roger Bogning 《Open Journal of Applied Sciences》 2024年第7期1730-1753,共24页
The waveguide which is at the center of our concerns in this work is a strongly flattened waveguide, that is to say characterized by a strong dispersion and in addition is strongly nonlinear. As this type of waveguide... The waveguide which is at the center of our concerns in this work is a strongly flattened waveguide, that is to say characterized by a strong dispersion and in addition is strongly nonlinear. As this type of waveguide contains multiple dispersion coefficients according to the degrees of spatial variation within it, our work in this article is to see how these dispersions and nonlinearities each influence the wave or the signal that can propagate in the waveguide. Since the partial differential equation which governs the dynamics of propagation in such transmission medium presents several dispersion and nonlinear coefficients, we check how they contribute to the choices of the solutions that we want them to verify this nonlinear partial differential equation. This effectively requires an adequate choice of the form of solution to be constructed. Thus, this article is based on three main pillars, namely: first of all, making a good choice of the solution function to be constructed, secondly, determining the exact solutions and, if necessary, remodeling the main equation such that it is possible;then check the impact of the dispersion and nonlinear coefficients on the solutions. Finally, the reliability of the solutions obtained is tested by a study of the propagation. Another very important aspect is the use of notions of probability to select the predominant solutions. 展开更多
关键词 Flattened Waveguide Solitary Wave Characteristic Coefficient Probabilities Propagation Nonlinear dispersIVE Partial Differential equation
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The classification of travelling wave solutions and superposition of multi-solutions to Camassa-Holm equation with dispersion 被引量:7
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作者 刘成仕 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第7期1832-1837,共6页
Under the travelling wave transformation, the Camassa-Holm equation with dispersion is reduced to an integrable ordinary differential equation (ODE), whose general solution can be obtained using the trick of one-par... Under the travelling wave transformation, the Camassa-Holm equation with dispersion is reduced to an integrable ordinary differential equation (ODE), whose general solution can be obtained using the trick of one-parameter group. Furthermore, by using a complete discrimination system for polynomial, the classification of all single travelling wave solutions to the Camassa-Holm equation with dispersion is obtained. In particular, an affine subspace structure in the set of the solutions of the reduced ODE is obtained. More generally, an implicit linear structure in the Camassa-Holm equation with dispersion is found. According to the linear structure, we obtain the superposition of multi-solutions to Camassa-Holm equation with dispersion. 展开更多
关键词 classification of travelling wave solution symmetry group Camassa-Holm equation with dispersion superposition of solutions
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PERIODIC BOUNDARY VALUE PROBLEM AND CAUCHY PROBLEM OF THE GENERALIZED CUBIC DOUBLE DISPERSION EQUATION 被引量:1
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作者 陈国旺 薛红霞 《Acta Mathematica Scientia》 SCIE CSCD 2008年第3期573-587,共15页
In this article, the existence, uniqueness and regularities of the global generalized solution and global classical solution for the periodic boundary value problem and the Cauchy problem of the general cubic double d... In this article, the existence, uniqueness and regularities of the global generalized solution and global classical solution for the periodic boundary value problem and the Cauchy problem of the general cubic double dispersion equationutt - uxx - auxxtt + bux4 - duxxt = f(u)xxare proved, and the sufficient conditions of blow-up of the solutions for the Cauchy problems in finite time are given. 展开更多
关键词 The generalized cubic double dispersion equation Cauchy problem existence and uniqueness of global solution nonexistence of global solution
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Comparison of Finite Difference Schemes for the Wave Equation Based on Dispersion 被引量:1
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作者 Yahya Ali Abdulkadir 《Journal of Applied Mathematics and Physics》 2015年第11期1544-1562,共19页
Finite difference techniques are widely used for the numerical simulation of time-dependent partial differential equations. In order to get better accuracy at low computational cost, researchers have attempted to deve... Finite difference techniques are widely used for the numerical simulation of time-dependent partial differential equations. In order to get better accuracy at low computational cost, researchers have attempted to develop higher order methods by improving other lower order methods. However, these types of methods usually suffer from a high degree of numerical dispersion. In this paper, we review three higher order finite difference methods, higher order compact (HOC), compact Padé based (CPD) and non-compact Padé based (NCPD) schemes for the acoustic wave equation. We present the stability analysis of the three schemes and derive dispersion characteristics for these schemes. The effects of Courant Friedrichs Lewy (CFL) number, propagation angle and number of cells per wavelength on dispersion are studied. 展开更多
关键词 WAVE equation FINITE DIFFERENCE Methods dispersion
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Dispersion equation of magnetoelastic shear waves in irregular monoclinic layer
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作者 A.CHATTOPADHYAY S.GUPTA +1 位作者 S.A.SAHU A.K.SINGH 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第5期571-586,共16页
This paper studies the propagation of horizontally polarized shear waves in an internal magnetoelastic monoclinic stratum with irregularity in lower interface. The stratum is sandwiched between two magnetoelastic mono... This paper studies the propagation of horizontally polarized shear waves in an internal magnetoelastic monoclinic stratum with irregularity in lower interface. The stratum is sandwiched between two magnetoelastic monoclinic semi-infinite media. Dispersion equation is obtained in a closed form. In the absence of magnetic field and irregularity of the medium, the dispersion equation agrees with the equation of classical case in three layered media. The effects of magnetic field and size of irregularity on the phase velocity are depicted by means of graphs. 展开更多
关键词 shear wave MAGNETOELASTIC MONOCLINIC IRREGULARITY dispersion equation PERTURBATION
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G-type dispersion equation under suppressed rigid boundary:analytic approach
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作者 S.K.VISHWAKARMA Runzhang XU 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2016年第4期501-512,共12页
This paper studies dispersion of a G-type earthquake wave under the influence of a suppressed rigid boundary. Inside the Earth, the density and rigidity of the crustal layer and the mantle of the Earth vary exponentia... This paper studies dispersion of a G-type earthquake wave under the influence of a suppressed rigid boundary. Inside the Earth, the density and rigidity of the crustal layer and the mantle of the Earth vary exponentially and periodically along the depth. The displacements of the wave are found in the individual medium followed by a dispersion equation using a suitable analytic approach and a boundary condition. The prominent effect of inhomogeneity contained in the media, the rigid boundary plane, and the initial stress on the phase and group velocities is shown graphically. 展开更多
关键词 G-type wave analytic approach dispersion equation group velocity rigid boundary
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Dispersion Equation of Low-Frequency Waves Driven by Temperature Anisotropy
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作者 陈玲 吴德金 《Plasma Science and Technology》 SCIE EI CAS CSCD 2012年第10期880-885,共6页
The plasma temperature (or the kinetic pressure) anisotropy is an intrinsic characteristic of a collisionless magnetized plasma. In this paper, based on the two-fluid model, a dispersion equation of low-frequency ... The plasma temperature (or the kinetic pressure) anisotropy is an intrinsic characteristic of a collisionless magnetized plasma. In this paper, based on the two-fluid model, a dispersion equation of low-frequency (ω〈〈ωci, ωci the ion gyrofrequency) waves, including the plasma temperature anisotropy effect, is presented. We investigate the properties of low-frequency waves when the parallel temperature exceeds the perpendicular temperature, and especially their dependence on the propagation angle, pressure anisotropy, and energy closures. The results show that both the instable Alfven and slow modes are purely growing. The growth rate of the Alfven wave is not affected by the propagation angle or energy closures, while that of the slow wave depends sensitively on the propagation angle and energy closures as well as pressure anisotropy. The fast wave is always stable. We also show how to elaborate the symbolic calculation of the dispersion equation performed using Mathematica Notebook. 展开更多
关键词 dispersion equation low-frequency waves temperature anisotropy
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An extended time-dependent numerical model of the mild-slope equation with weakly nonlinear amplitude dispersion
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作者 ZHAO Hongjun SONG Zhiyao +1 位作者 XU Fumin LI Ruijie 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2010年第2期5-13,共9页
In the present paper, by introducing the effective wave elevation, we transform the extended elliptic mild-slope equation with bottom friction, wave breaking and steep or rapidly varying bottom topography to the simpl... In the present paper, by introducing the effective wave elevation, we transform the extended elliptic mild-slope equation with bottom friction, wave breaking and steep or rapidly varying bottom topography to the simplest time-dependent hyperbolic equation. Based on this equation and the empirical nonlinear amplitude dispersion relation proposed by Li et al. (2003), the numerical scheme is established. Error analysis by Taylor expansion method shows that the numerical stability of the present model succeeds the merits in Song et al. (2007)'s model because of the introduced dissipation terms. For the purpose of verifying its performance on wave nonlinearity, rapidly varying topography and wave breaking, the present model is applied to study: (1) wave refraction and diffraction over a submerged elliptic shoal on a slope (Berkhoff et al., 1982); (2) Bragg reflection of monochromatic waves from the sinusoidal ripples (Davies and Heathershaw, 1985); (3) wave transformation near a shore attached breakwater (Watanabe and Maruyama, 1986). Comparisons of the numerical solutions with the experimental or theoretical ones or with those of other models (REF/DIF model and FUNWAVE model) show good results, which indicate that the present model is capable of giving favorably predictions of wave refraction, diffraction, reflection, shoaling, bottom friction, breaking energy dissipation and weak nonlinearity in the near shore zone. 展开更多
关键词 TIME-DEPENDENT mild-slope equation varying topography bottom friction nonlinear amplitude dispersion steep or rapidly wave breaking
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Lie Symmetry Reductions and Exact Solutions of a Multidimensional Double Dispersion Equation
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作者 Jiali Yu Fuzhi Li Lianbing She 《Applied Mathematics》 2017年第5期712-723,共12页
In this paper, based on classical Lie group method, we study a multidimensional double dispersion equation, and get its infinitesimal generator, symmetry group and similarity reductions. In particular, similarity solu... In this paper, based on classical Lie group method, we study a multidimensional double dispersion equation, and get its infinitesimal generator, symmetry group and similarity reductions. In particular, similarity solutions and travelling wave solutions of the multidimensional double dispersion equation are derived from the reduction equations. 展开更多
关键词 Lie Group MULTIDIMENSIONAL DOUBLE dispersion equation Similarity SOLUTIONS TRAVELLING Wave SOLUTIONS
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Chebyshev Pseudo-Spectral Method for Solving Fractional Advection-Dispersion Equation 被引量:2
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作者 N. H. Sweilam M. M. Khader M. Adel 《Applied Mathematics》 2014年第19期3240-3248,共9页
Fractional differential equations have recently been applied in various areas of engineering, science, finance, applied mathematics, bio-engineering and others. However, many researchers remain unaware of this field. ... Fractional differential equations have recently been applied in various areas of engineering, science, finance, applied mathematics, bio-engineering and others. However, many researchers remain unaware of this field. In this paper, an efficient numerical method for solving the fractional Advection-dispersion equation (ADE) is considered. The fractional derivative is described in the Caputo sense. The method is based on Chebyshev approximations. The properties of Chebyshev polynomials are used to reduce ADE to a system of ordinary differential equations, which are solved using the finite difference method (FDM). Moreover, the convergence analysis and an upper bound of the error for the derived formula are given. Numerical solutions of ADE are presented and the results are compared with the exact solution. 展开更多
关键词 FRACTIONAL ADVECTION-dispersion equation Caputo FRACTIONAL DERIVATIVE Finite DIFFERENCE METHOD CHEBYSHEV Pseudo-Spectral METHOD Convergence Analysis
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Advection Dispersion Equation and BMO Space
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作者 Kan Zhang Tieliang Wang Xue Feng 《Journal of Applied Mathematics and Physics》 2013年第5期121-127,共7页
In this paper, we provide a new way of characterizing the upper and lower bound for the concentration and the gradient of concentration in advection dispersion equation under the condition that source term, concentrat... In this paper, we provide a new way of characterizing the upper and lower bound for the concentration and the gradient of concentration in advection dispersion equation under the condition that source term, concentration and stirring term belong to BMO space. 展开更多
关键词 Advection dispersion equation BMO CONCENTRATION
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High Order Numerical Code for Hyperbolic Mild-slope Equations with Nonlinear Dispersion Relation
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作者 IU Zhongbo ZHANG Rixiang CHEN Bing 《Journal of Ocean University of China》 SCIE CAS 2007年第4期421-423,共3页
Based on the hyperbolic mild-slope equations derived by Copeland (1985), a numerical model is established in unstag- gered grids. A composite 4 th-order Adam-Bashforth-Moulton (ABM) scheme is used to solve the model i... Based on the hyperbolic mild-slope equations derived by Copeland (1985), a numerical model is established in unstag- gered grids. A composite 4 th-order Adam-Bashforth-Moulton (ABM) scheme is used to solve the model in the time domain. Terms involving the first order spatial derivatives are differenced to O ( Δx )4accuracy utilizing a five-point formula. The nonlinear dispersion relationship proposed by Kirby and Dalrymple (1986) is used to consider the nonlinear effect. A numerical test is performed upon wave propagating over a typical shoal. The agreement between the numerical and the experimental results validates the present model. Biodistribution and applications are also summarized. 展开更多
关键词 hyperbolic mild-slope equations Adams-Bashforth-Moulton scheme nonlinear dispersion property WAVE
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Suppress numerical dispersion in reversetime migration of acoustic wave equation using optimal nearly analytic discrete method
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作者 Liu Ming-Zhu He Bing-Shoug 《Applied Geophysics》 SCIE CSCD 2020年第1期133-142,170,共11页
Using staggered-grid finite difference method to solve seismic wave equation,large spatial grid and high dominant frequency of source cause numerical dispersion,staggeredgrid finite difference method,which can reduce ... Using staggered-grid finite difference method to solve seismic wave equation,large spatial grid and high dominant frequency of source cause numerical dispersion,staggeredgrid finite difference method,which can reduce the step spatial size and increase the order of difference,will multiply the calculation amount and reduce the efficiency of solving wave equation.The optimal nearly analytic discrete(ONAD)method can accurately solve the wave equation by using the combination of displacement and gradient of spatial nodes to approach the spatial partial derivative under rough grid and high-frequency condition.In this study,the ONAD method is introduced into the field of reverse-time migration(RTM)for performing forward-and reverse-time extrapolation of a two-dimensional acoustic equation,and the RTM based on ONAD method is realized via normalized cross-correlation imaging condition,effectively suppressed the numerical dispersion and improved the imaging accuracy.Using ONAD method to image the groove model and SEG/EAGE salt dome model by RTM,and comparing with the migration sections obtained by staggered-grid finite difference method with the same time order 2 nd and space order 4 th,results show that the RTM based on ONAD method can effectively suppress numerical dispersion caused by the high frequency components in source and shot records,and archive accurate imaging of complex geological structures especially the fine structure,and the migration sections of the measured data show that ONAD method has practical application value. 展开更多
关键词 Acoustic wave equation RTM ONAD method numerical dispersion suppression
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The Dispersion Relation of Internal Wave Extended-Korteweg-de Vries Equation in a Two-Layer Fluid
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作者 Pingping Feng Xianghua Meng 《Journal of Applied Mathematics and Physics》 2021年第5期1056-1064,共9页
To understand the characteristics of ocean internal waves better, we study the dispersion relation of extended-Korteweg-de Vries (EKdV) equation with quadratic and cubic nonlinear terms in a two-layer fluid by using t... To understand the characteristics of ocean internal waves better, we study the dispersion relation of extended-Korteweg-de Vries (EKdV) equation with quadratic and cubic nonlinear terms in a two-layer fluid by using the Poincaré-Lighthill-Kuo (PLK) method which is one of the perturbation methods. Starting from the partial differential equation, the PLK method can be used to solve the dispersion relation of the equation. In this paper, we use PLK method to solve the equation and derive the dispersion relation of EKdV equation which is related to wave number and amplitude. Based on the dispersion relation obtained in this paper, the expressions of group velocity and phase velocity of the equation are obtained. Under the actual hydrological data, the influence of hydrological parameters on the dispersion relation for descending internal wave is discussed. It is hope that the obtained results will be helpful to the study of energy transfer and other internal wave parameters in the future. 展开更多
关键词 Ocean Internal Waves dispersion Relation Extended-Korteweg-de Vries equation Poincaré-Lighthill-Kuo Method
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Dispersion Equation in Non-uniform Optical Waveguide
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作者 ZHANG Jinwei(Jinan University, Guangzhou 510632,CHN) 《Semiconductor Photonics and Technology》 CAS 1996年第2期90-98,共9页
We study the WKB dispersion equation in non-uniform optical waveguide.There are three methods given in this paper:(1) method of Airy function;(2)method of connection formula;and(3) method of phase shift.At last we mak... We study the WKB dispersion equation in non-uniform optical waveguide.There are three methods given in this paper:(1) method of Airy function;(2)method of connection formula;and(3) method of phase shift.At last we make some remarks. 展开更多
关键词 Optical Waveguide dispersion equation WKB Approximate Method
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Stability and Convergence of an Implicit Difference Approximation for the Space Riesz Fractional Reaction-Dispersion Equation
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作者 Jinghua Chen Fawang Liu 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2007年第3期253-264,共12页
In this paper,we consider a Riesz space-fractional reaction-dispersion equation (RSFRDE).The RSFRDE is obtained from the classical reaction-dispersion equation by replacing the second-order space derivative with a Rie... In this paper,we consider a Riesz space-fractional reaction-dispersion equation (RSFRDE).The RSFRDE is obtained from the classical reaction-dispersion equation by replacing the second-order space derivative with a Riesz derivative of orderβ∈(1,2]. We propose an implicit finite difference approximation for RSFRDE.The stability and convergence of the finite difference approximations are analyzed.Numerical results are found in good agreement with the theoretical analysis. 展开更多
关键词 分数次导数 分形反应-色散方程 隐式有限差分近似 稳定性 收敛性
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Exact travelling wave solutions for (1+ 1)-dimensional dispersive long wave equation 被引量:15
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作者 刘成仕 《Chinese Physics B》 SCIE EI CAS CSCD 2005年第9期1710-1715,共6页
A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a (1+1)-dimensional dispersive long wave equation with general coefficients to an elementary integral fo... A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a (1+1)-dimensional dispersive long wave equation with general coefficients to an elementary integral form and obtained its all possible exact travelling wave solutions including rational function type solutions, solitary wave solutions, triangle function type periodic solutions and Jacobian elliptic functions double periodic solutions. This method can be also applied to many other similar problems. 展开更多
关键词 complete discrimination system for polynomial (1+1)-dimensional dispersive long wave equation travelling wave solution
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Exotic Localized Coherent Structures of the (2+1)—Dimensional Dispersive Long—Wave Equation 被引量:11
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作者 ZHANGJie-Fang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2002年第3期277-282,共6页
This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structures in the (2+1)-dimensional dispersive long-wave equations . Starting from the homogeneous ba... This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structures in the (2+1)-dimensional dispersive long-wave equations . Starting from the homogeneous balance method, we find that the richness of the localized coherent structures of the model is caused by the entrance of two variable-separated arbitrary functions. For some special selections of the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, breathers, instantons and ring solitons. 展开更多
关键词 extended homogeneous balance method coherent soliton structures dispersive long-wave equation the (2+1)-dimensions
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Multiple Soliton Solutions of the Dispersive Long-Wave Equations 被引量:2
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作者 ZHANG Jie-fang 《Chinese Physics Letters》 SCIE CAS CSCD 1999年第1期4-5,共2页
Using a simple homogeneous balance method,which is very concise and primary,we find the multiple soliton solutions of the dispersive long-wave equations.The method can be generalized to deal with the higher dimensiona... Using a simple homogeneous balance method,which is very concise and primary,we find the multiple soliton solutions of the dispersive long-wave equations.The method can be generalized to deal with the higher dimensional dispersive long-wave equations and other class of nonlinear equation. 展开更多
关键词 equation. equations. dispersIVE
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