共查询到20条相似文献,搜索用时 15 毫秒
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In this paper, a two-step ansatz is proposed, which leads to some new solutions to two coupled nonlinear physical equations. 相似文献
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Exact solutions for the coupled Klein-Gordon-Schrǒdinger equations using the extended F-expansion method 下载免费PDF全文
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. 相似文献
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In this article,we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations.We use the improved(G’/G)-expansion function method to calculate the exact solutions to the time-and space-fractional derivative foam drainage equation and the time-and space-fractional derivative nonlinear KdV equation.This method is efficient and powerful for solving wide classes of nonlinear evolution fractional order equations. 相似文献
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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. 相似文献
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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. 相似文献
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Exact travelling wave solutions to some nonlinear equations of fifth order derivatives are derived by using some accurate ansatz methods. 相似文献
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V.A. Vladimirov 《Reports on Mathematical Physics》2004,54(2):261-271
A direct algebraic method of obtaining exact solutions to nonlinear PDE's is applied to certain set of nonlinear nonlocal evolutionary equations, including nonlinear telegraph equation, hyperbolic generalization of Burgers equation and some spatially nonlocal hydrodynamic-type model. Special attention is paid to the construction of the kink-like and soliton-like solutions. 相似文献
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Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear ordinary differential equations 总被引:2,自引:2,他引:0
The problem of preserving fidelity in numerical computation of nonlinear ordinary differential equations is studied in terms
of preserving local differential structure and approximating global integration structure of the dynamical system. The ordinary
differential equations are lifted to the corresponding partial differential equations in the framework of algebraic dynamics,
and a new algorithm—algebraic dynamics algorithm is proposed based on the exact analytical solutions of the ordinary differential
equations by the algebraic dynamics method. In the new algorithm, the time evolution of the ordinary differential system is
described locally by the time translation operator and globally by the time evolution operator. The exact analytical piece-like
solution of the ordinary differential equations is expressed in terms of Taylor series with a local convergent radius, and
its finite order truncation leads to the new numerical algorithm with a controllable precision better than Runge Kutta Algorithm
and Symplectic Geometric Algorithm. 相似文献
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In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space–time fractional modified Benjamin–Bona–Mahoney(m BBM) equation, the time fractional m Kd V equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions: amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional derivatives are described in the modified Riemann–Liouville sense. 相似文献
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In this paper, an extended Riccati sub-ODE method is proposed to establish new exact solutions for fractional differential-difference equations in the sense of modified Riemann-Liouville derivative. By a fractional complex transformation, a given fractional differential-difference equation can be turned into another differential-difference equation of integer order. The validity of the method is illustrated by applying it to solve the fractional Hybrid lattice equation and the fractional relativistic Toda lattice system. As a result, some new exact solutions including hyperbolic function solutions, trigonometric function solutions and rational solutions are established. 相似文献
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Using functional derivative technique in quantum field theory, the algebraic dynamics approach for solution of ordinary differential
evolution equations was generalized to treat partial differential evolution equations. The partial differential evolution
equations were lifted to the corresponding functional partial differential equations in functional space by introducing the
time translation operator. The functional partial differential evolution equations were solved by algebraic dynamics. The
algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact
analytical solutions, a new numerical algorithm—algebraic dynamics algorithm was proposed for partial differential evolution
equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer
numerical experiments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic
dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution
equations both analytically and numerically.
Supported by the National Natural Science Foundation of China (Grant Nos. 10375039, 10775100 and 90503008), the Doctoral Program
Foundation of the Ministry of Education of China, and the Center of Nuclear Physics of HIRFL of China 相似文献
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The symmetry reduction method based on the Fr′echet derivative of differential operators is applied to investigate symmetries of the Einstein-Maxwell field equations for magnetostatic fields, which is a coupled system of nonlinear partial differential equations of the second order. The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations. Some of the reduced systems are further studied to obtain the exact solutions. 相似文献
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The symmetry reduction method based on the Fréchet derivative of differential operators is applied to investigate symmetries of the Einstein-Maxwell field equations for magnetostatic fields, which is a coupled system of nonlinear partial differential equations of the second order. The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations. Some of the reduced systems are further studied to obtain the exact solutions. 相似文献
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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. 相似文献