共查询到20条相似文献,搜索用时 62 毫秒
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In this Letter, the Fan sub-equation method is used to construct exact solutions of a generalized Hirota-Satsuma coupled KdV equation. Many exact traveling wave solutions are successfully obtained, which contain more general solitary wave solutions and Jacobian elliptic function solutions with double periods. This method is straightforward and concise, and it can also be applied to other nonlinear evolution equations. 相似文献
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《Waves in Random and Complex Media》2013,23(2):189-196
AbstractIn this study, a new method called improved Bernoulli sub-equation function method has been proposed. This method is based on the Bernoulli sub-ODE method. After we mention the general properties of proposed method, we apply this algorithm to the (2 + 1)-dimensional Boiti–Leon–Pempinelli equation system. This gives us some new prototype solutions such as exponential and rational function solutions. Then, we have plotted two- and three-dimensional surfaces of analytical solutions. Finally, we have submitted a comprehensive conclusion. 相似文献
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An extended mapping deformation method is proposed for finding new exact travelling wave solutions of nonlinear partial differential equations (PDEs). The key idea of this method is to take full advantage of the simple algebraic mapping relation between the solutions of the PDEs and those of the cubic nonlinear Klein-Gordon equation. This is applied to solve a system of variant Boussinesq equations. As a result, many explicit and exact solutions are obtained, including solitary wave solutions, periodic wave solutions, Jacobian elliptic function solutions and other exact solutions. 相似文献
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E. Tala-Tebue Z.I. Djoufack S.B. Yamgoué A. Kenfack-Jiotsa T.C. Kofané 《Chinese Journal of Physics (Taipei)》2018,56(3):1010-1020
This paper presents many new solutions of a modified Zakharov–Kuznetsov equation obtained by using the Jacobi elliptical function method. This equation is shown to model a two dimensional discrete electrical lattice. The solutions reported herein are of varied types and include hyperbolic and trigonometric solutions, as well as kink and bell-shaped solitons. The comparison of our results to well-known ones is done. The method used here is very simple and concise and can be also applied to other nonlinear partial differential equations. More importantly, the solutions found in this work can have significant applications in telecommunication systems where solitons are used to codify data. 相似文献
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New doubly periodic and multiple soliton solutions of the generalized (3+l)-dimensional KP equation with variable coefficients 下载免费PDF全文
A new generalized Jacobi elliptic function method is used to construct the exact travelling wave solutions of nonlinear partial differential equations (PDEs) in a unified way. The main idea of this method is to take full advantage of the elliptic equation which has more new solutions. More new doubly periodic and multiple soliton solutions are obtained for the generalized (3+1)-dimensional Kronig-Penny (KP) equation with variable coefficients. This method can be applied to other equations with variable coefficients. 相似文献
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In this paper, we present a method to solve difference differential equation(s). As an example, we apply
this method to discrete KdV equation and Ablowitz-Ladik lattice
equation. As a result, many exact solutions are obtained with the
help of Maple including soliton solutions presented by hyperbolic
functions sinh and cosh, periodic solutions presented by
sin and cos and rational solutions. This method can also be
used to other nonlinear difference-differential equation(s). 相似文献
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提出了一种新的水平变化波导中声场的耦合简正波求解方法,该方法能够处理二维点源和线源问题,提供声场的双向解。该方法利用全局矩阵(DGM)一次性求解耦合模式的系数,消除了传播矩阵递推求解中存在的误差累积问题;此外,改善了现有模型中对距离函数的归一化方法,从而避免了泄露模式指数增长导致的数值溢出问题。本文还给出了绝对软海底理想波导中耦合矩阵的闭合表达式,并分析了单个阶梯下简正波耦合现象。此外,本文还计算了理想楔形波导中的声传播问题(ASA标准问题),并与解析解及COUPLE07计算结果进行了比较,结果表明该方法是一种稳定、精确的水平变化波导中的声场计算方法。 相似文献
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Studying compactons, solitons, solitary patterns and periodic solutions is important in nonlinear phenomena. In this paper we study nonlinear variants of the Kadomtsev–Petviashvili (KP) and the Korteweg–de Vries (KdV) equations with positive and negative exponents. The functional variable method is used to establish compactons, solitons, solitary patterns and periodic solutions for these variants. This method is a powerful tool for searching exact travelling solutions in closed form. 相似文献
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This study is related to new soliton solutions of Davey–Stewartson equation (DSE) with power-law nonlinearity. The generalized Kudryashov method which is one of the analytical methods has been used for finding exact solutions of this equation. By using this method, dark soliton solutions of DSE have been found. Also, by using Mathematica Release 9, some graphical representations have been done to analyze the motion of these solutions. 相似文献
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The dynamics of nonstationary solutions in one-dimensional two-component Bose-Einstein condensates 下载免费PDF全文
This paper investigates the dynamical properties of nonstationary solutions in one-dimensional two-component Bose-Einstein condensates.It gives three kinds of stationary solutions to this model and develops a general method of constructing nonstationary solutions.It obtains the unique features about general evolution and soliton evolution of nonstationary solutions in this model. 相似文献
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FENG Qing-Hua 《理论物理通讯》2014,62(2):167-172
In this paper, a new fractional projective Riccati equation method is proposed to establish exact solutions for fractional partial differential equations in the sense of modified Riemann—Liouville derivative. This method can be seen as the fractional version of the known projective Riccati equation method. For illustrating the validity of this method, we apply this method to solve the space—time fractional Whitham—Broer—Kaup (WBK) equations and the nonlinear fractional Sharma—Tasso—Olever (STO) equation, and as a result, some new exact solutions for them are obtained. 相似文献
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In this paper,a new extended complex tanh-function method is presented for constructing traveling wave,non-traveling wave,and coefficient functions' soliton-like solutions of nonlinear equations.This method is nore powerful than the complex tanh-function method [Chaos,Solitons and Fractals 20 (2004) 1037].Abundant new solutions of (2 1)-dimensional Hirota equation are obtained by using this method and symbolic computation system Maple. 相似文献
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《Waves in Random and Complex Media》2013,23(4):775-790
ABSTRACTThe Klein–Gordon equation plays an important role in mathematical physics. In this paper, a direct method which is very effective, simple, and convenient, is presented for solving the conformable fractional Klein–Gordon equation. Using this analytic method, the exact solutions of this equation are found in terms of the Jacobi elliptic functions. This method is applied to both time and space fractional equations. Some solutions are also illustrated by the graphics. 相似文献
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The \(\phi ^{6}\)-model expansion method combined with the conformable time-fractional derivative is applied in this paper for finding many new exact solutions including Jacobi elliptic function solutions, solitary wave solutions, trigonometric function solutions and other solutions to the nonlinear conformable time-fractional Schrödinger equation with fourth-order dispersion and parabolic law nonlinearity. This method presents a wider applicability for handling the nonlinear partial differential equations. Comparing our results with the well-known results are given. 相似文献
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In this paper, we find exact solutions of some nonlinear evolution equations by using generalized tanh–coth method. Three nonlinear models of physical significance, i.e. the Cahn–Hilliard equation, the Allen–Cahn equation and the steady-state equation with a cubic nonlinearity are considered and their exact solutions are obtained. From the general solutions, other well-known results are also derived. Also in this paper, we shall compare the generalized tanh–coth method and generalized (G ′/G )-expansion method to solve partial differential equations (PDEs) and ordinary differential equations (ODEs). Abundant exact travelling wave solutions including solitons, kink, periodic and rational solutions have been found. These solutions might play important roles in engineering fields. The generalized tanh–coth method was used to construct periodic wave and solitary wave solutions of nonlinear evolution equations. This method is developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that the generalized tanh–coth method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear problems. 相似文献
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A new variable coefficient algebraic method and non-travelling wave solutions of nonlinear equations 下载免费PDF全文
In this paper, a new auxiliary equation method is presented of constructing more new non-travelling wave solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than projective Riccati equation method. In order to illustrate the validity and the advantages of the method, (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation is employed and many new double periodic non-travelling wave solutions are obtained. This algorithm can also be applied to other nonlinear differential equations. 相似文献
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SCHMIDT Henrik 《声学学报:英文版》2012,(4):371-391
##正##An efficient,accurate,and numerically stable coupled-mode solution is presented for acoustic propagation in a range-dependent waveguide.This method is numerically stable due to the appropriately normalized range solutions introduced in the formulation.In addition,by combining a forward marching and a backward marching,this method provides accurate solutions for range-dependent propagation problems,especially those characterized by large bottom slope angle and/or high impedance contrast between water and the bottom.Furthermore,this two-way solution also provides high efficiency,which is achieved by applying the single-scatter approximation.Numerical examples are also provided to demonstrate the efficiency,accuracy, and stability of this method. 相似文献