共查询到20条相似文献,搜索用时 15 毫秒
1.
ZHANG Yuan-Yuan ZHENG Ying ZHANG Hong-Qing 《理论物理通讯》2006,46(3):407-414
In this paper, we extend the multiple Riccati equations rational expansion method by introducing a new ansatz. Using this method, many complexiton solutions of the (2+ 1 )-dimensional Nizhnik-Novikov-Veselov equations are obtained which include various combination of hyperbolic and trigonometric periodic function solutions, various combination of hyperbolic and rational function solutions, various combination of trigonometric periodic and rational function solutions, etc. The method can be also used to solve other nonlinear partial differential equations. 相似文献
2.
In this pager a pure algebraic method implemented in a computer
algebraic system, named multiple Riccati equations rational
expansion method, is presented to construct a novel class of
complexiton solutions to integrable equations and nonintegrable
equations. By solving the (2+1)-dimensional dispersive long wave
equation, it obtains many new types of complexiton solutions such as
various combination of trigonometric periodic and hyperbolic
function solutions, various combination of trigonometric periodic
and rational function solutions, various combination of hyperbolic
and rational function solutions, etc. 相似文献
3.
By means of two different Riccati
equations with different parameters as subequation in the components of finite rational expansion method, new complexiton solutions for the (1+1)-dimensional dispersive long wave equation are successfully constructed, which include various combination of
trigonometric periodic and hyperbolic function solutions, various
combination of trigonometric periodic and rational function
solutions, and various combination of hyperbolic and rational
function solutions. 相似文献
4.
Mohammed K. Elboree 《理论物理通讯》2015,64(4):379-390
In this paper, we investigate the traveling wave solutions for the nonlinear dispersive equation, Korteweg-de Vries Zakharov-Kuznetsov (KdV-ZK) equation and complex coupled KdV system by using extended simplest equation method, and then derive the hyperbolic function solutions include soliton solutions, trigonometric function solutions include periodic solutions with special values for double parameters and rational solutions. The properties of such solutions are shown by figures. The results show that this method is an effective and a powerful tool for handling the solutions of nonlinear partial differential equations (NLEEs) in mathematical physics. 相似文献
5.
WANG Yue-Ming LI Xiang-Zheng YANG Sen WANG Ming-Liang 《理论物理通讯》2005,44(3):396-400
We present an F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed recently. By using the F-expansion, without calculating Jacobi elliptic functions, we obtain simultaneously many periodic wave solutions expressed by various Jacobi elliptic functions for the variant Boussinesq equations. When the modulus m approaches 1 and O, the hyperbolic function solutions (including the solitary wave solutions) and trigonometric solutions are also given respectively. 相似文献
6.
We present an F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed recently. By using the F-expansion, without calculating Jacobi elliptic functions, we obtain simultaneously many periodic wave solutions expressed by various Jacobi elliptic functions for the variant Boussinesq equations. When the modulus m approaches 1 and 0, the hyperbolic function solutions (including the solitary wave solutions) and trigonometric solutions are also given respectively. 相似文献
7.
In this paper, we use our method to solve the extended Lotka--Volterra equation and
discrete KdV equation. With the help of Maple, we obtain a number of exact solutions
to the two equations including soliton solutions presented by hyperbolic functions
of \sinh and \cosh, periodic solutions presented by trigonometric functions of
\sin and \cos, and rational solutions. This method can be used to solve some
other nonlinear difference--differential equations. 相似文献
8.
With the aid of computerized symbolic computation, an improved F-expansion method is presented to uniformly construct more new exact doubly periodic solutions in terms of rational formal Jacobi elliptic function of nonlinear partial differential equations (NPDEs). The coupled
Drinfel'd-Sokolov-Wilson equation is chosen to illustrate the method. As a
result, we can successfully obtain abundant new doubly periodic
solutions without calculating various Jacobi elliptic functions. In
the limit cases, the rational solitary wave solutions and trigonometric function solutions are obtained as well. 相似文献
9.
An improved algorithm is devised for using Fan sub-equation method to solve Wick-type stochastic partial differential equations. Applying the improved algorithm to the Wick-type generalized stochastic KdV equation, we obtain more general Jacobi and Weierstrass elliptic function solutions, hyperbolic and trigonometric function solutions, exponential function solutions and rational solutions. 相似文献
10.
In this paper, we construct exact solutions for the (2+1)-dimensional Boiti-Leon-Pempinelle equation by using the (G'/G)-expansion method, and with the help of Maple. As a result, non-travelling wave solutions with three arbitrary functions are obtained including hyperbolic function solutions, trigonometric function solutions, and rational solutions. This method can beapplied to other higher-dimensional nonlinear partial differential equations. 相似文献
11.
The general Jacobi elliptic function expansion method is developed and extended to construct doubly periodic wave solutions
for discrete nonlinear equations. Applying this method, many exact elliptic function doubly periodic wave solutions are obtained
for Ablowitz–Ladik lattice system. When the modulus m→1 or m→0, these solutions degenerate into hyperbolic function solutions and trigonometric function solutions respectively. In long
wave limit, solitonic solutions including bright soliton and dark soliton solutions are also obtained. 相似文献
12.
Differential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous.Although a considerable amount of research has been carried out in the field of nonlinear differential-difference equations,the majority of the results deal with polynomial types.Limited research has been reported regarding such equations of rational type.In this paper we present an adaptation of the(G /G)-expansion method to solve nonlinear rational differential-difference equations.The procedure is demonstrated using two distinct equations.Our approach allows one to construct three types of exact traveling wave solutions(hyperbolic,trigonometric,and rational) by means of the simplified form of the auxiliary equation method with reduced parameters.Our analysis leads to analytic solutions in terms of topological solitons and singular periodic functions as well. 相似文献
13.
14.
A direct method, called the transformed rational function method, is used to construct more types of exact solutions of nonlinear
partial differential equations by introducing new and more general rational functions. To illustrate the validity and advantages
of the introduced general rational functions, the (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama (YTSF) equation is considered
and new travelling wave solutions are obtained in a uniform way. Some of the obtained solutions, namely exponential function
solutions, hyperbolic function solutions, trigonometric function solutions, Jacobi elliptic function solutions and rational
solutions, contain an explicit linear function of the independent variables involved in the potential YTSF equation. It is
shown that the transformed rational function method provides more powerful mathematical tool for solving nonlinear partial
differential equations. 相似文献
15.
16.
Taking the Konopelchenko-Dubrovsky system as a simple example, some families
of rational formal hyperbolic function solutions, rational formal
triangular periodic solutions, and rational solutions are
constructed by using the extended Riccati equation rational
expansion method presented by us. The method can also be applied
to solve more nonlinear partial differential equation or equations. 相似文献
17.
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
18.
This study investigates the perturbed Chen–Lee–Liu model that represents the propagation of an optical pulse in plasma and optical fiber. The generalized exponential rational function method is used for this purpose. As a result, we obtain some non-trivial solutions such as the optical singular, periodic, hyperbolic, exponential, trigonometric soliton solutions. We aim to express the pulse propagation of the generated solutions, by taking specific values for the free parameters existed in the obtained solutions. The obtained results show that the generalized exponential rational function technique is applicable, simple and effective to get the solutions of nonlinear engineering and physical problems. Moreover, the acquired solutions display rich dynamical evolutions that are important in practical applications. 相似文献
19.
We present an extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics. By using extended F-expansion method, many
periodic wave solutions expressed by various Jacobi elliptic functions for the Klein-Gordon-Schrödinger equations are obtained. In the limit cases, the solitary wave solutions and
trigonometric function solutions for the equations are also
obtained. 相似文献
20.
In this paper, an extended multiple (G′/G)-expansion method is proposed to seek exact solutions of nonlinear evolution equations. The validity and advantages of the
proposed method is illustrated by its applications to the Sharma–Tasso–Olver equation, the sixth-order Ramani equation, the
generalized shallow water wave equation, the Caudrey–Dodd–Gibbon–Sawada–Kotera equation, the sixth-order Boussinesq equation
and the Hirota–Satsuma equations. As a result, various complexiton solutions consisting of hyperbolic functions, trigonometric
functions, rational functions and their mixture with parameters are obtained. When some parameters are taken as special values,
the known double solitary-like wave solutions are derived from the double hyperbolic function solution. In addition, this
method can also be used to deal with some high-dimensional and variable coefficients’ nonlinear evolution equations. 相似文献