共查询到20条相似文献,搜索用时 296 毫秒
1.
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
2.
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
3.
The simplest formulas connecting Jacobi elliptic functions with different modulus parameters were first obtained over two
hundred years ago by John Landen. His approach was to change integration variables in elliptic integrals. We show that Landen’s
formulas and their subsequent generalizations can also be obtained from a different approach, using which we also obtain several
new Landen transformations. Our new method is based on recently obtained periodic solutions of physically interesting non-linear
differential equations and remarkable new cyclic identities involving Jacobi elliptic functions. 相似文献
4.
We consider a combined Korteweg–deVries and Boussinesq equation governing long surface waves in shallow water. Considering traveling wave solutions, the basic equations will be reduced to a second order ordinary differential equation. Using the Lie group of transformations we reduce it to a first order ordinary differential equation and employ a direct method to derive its periodic solutions in terms of Jacobian elliptic functions and their corresponding solitary wave and explode decay mode solutions. 相似文献
5.
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
6.
With the aid of computerized symbolic computation, a new elliptic function rational expansion method is presented by means of a new general ansatz, in which periodic solutions of nonlinear partial differential equations that can be expressed as a finite Laurent series of some of 12 Jacobi elliptic functions, is more powerful than exiting Jacobi elliptic function methods and is very powerful to uniformly construct more new exact periodic solutions in terms of rational formal Jacobi elliptic function solution of nonlinear partial differential equations. As an application of the method, we choose a (2+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by most existing Jacobi elliptic function methods and find other new and more general solutions at the same time. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition. 相似文献
7.
An extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics is presented, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed more recently. By using the homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by Jacobi elliptic functions for the coupled KdV equations are derived. In the limit cases, the solitary wave solutions and the other type of travelling wave solutions for the system are also obtained. 相似文献
8.
New Exact Solutions to Long-Short Wave Interaction Equations 总被引:1,自引:0,他引:1
TIAN Ying-Hui CHEN Han-Lin LIU Xi-Qiang 《理论物理通讯》2006,46(3):397-402
New exact solutions expressed by the Jacobi elliptic functions are obtained to the long-short wave interaction equations by using the modified F-expansion method. In the limit case, solitary wave solutions and triangular periodic wave solutions are obtained as well. 相似文献
9.
New exact solutions expressed by the Jacobi elliptic functions are obtained to the long-short wave interaction equations by using the modified F-expansion method. In the limit case, solitary wave solutions and triangular periodic wave solutions are obtained as well. 相似文献
10.
New exact solutions expressed by the Jacobi elliptic
functions are obtained to the (2+1)-dimensional dispersive long-wave
equations by using the modified F-expansion method. In the limit case, new
solitary wave solutions and triangular periodic wave solutions are obtained
as well. 相似文献
11.
Solutions to the equations describing materials with competing quadratic and cubic nonlinearities
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The Lie group theoretical method is used to study the equations
describing materials with competing quadratic and cubic
nonlinearities. The equations share some of the nice properties of
soliton equations. From the elliptic functions expansion method, we
obtain large families of analytical solutions, in special cases, we
have the periodic, kink and solitary solutions of the equations.
Furthermore, we investigate the stability of these solutions under
the perturbation of amplitude noises by numerical simulation. 相似文献
12.
ZHENG Chun-Long 《理论物理通讯》2004,41(3):391-396
By means of the standard truncated Painlev\'{e} expansion and a variable
separation approach, a general variable separation solution of the
generalized Burgers system is derived. In addition to the usual
localized coherent soliton excitations like dromions, lumps,
rings, breathers, instantons, oscillating soliton excitations,
peakons, foldons, and previously revealed chaotic and fractal
localized solutions, some new types of excitations --- compacton and
Jacobi periodic wave solutions are obtained by introducing
appropriate lower dimensional piecewise smooth
functions and Jacobi elliptic
functions. 相似文献
13.
In this paper, new basic functions, which are composed of three
basic Jacobi elliptic functions, are chosen as components of
finite expansion. This finite expansion can be taken as an ansatz
and applied to solve nonlinear wave equations. As an example, mKdV
equation is solved, and more new rational form solutions are
derived, such as periodic solutions of rational form, solitary
wave solutions of rational form, and so on. 相似文献
14.
The stability and dynamics of a new class of periodic solutions is investigated when a degenerate optical parametric oscillator system is forced by an external pumping field with a periodic spatial profile modeled by Jacobi elliptic functions. Both sinusoidal behavior as well as localized hyperbolic (front and pulse) behavior can be considered in this model. The stability and bifurcation behaviors of these transverse electromagnetic structures are studied numerically. The periodic solutions are shown to be stabilized by the nonlinear parametric interaction between the pump and signal fields interacting with the cavity diffraction, attenuation, and periodic external pumping. Specifically, sinusoidal solutions result in robust and stable configurations while well-separated and more localized field structures often undergo bifurcation to new steady-state solutions having the same period as the external forcing. Extensive numerical simulations and studies of the solutions are provided. 相似文献
15.
通过把十二个Jacobi椭圆函数分类成四组,提出了新的广泛的Jacobi椭圆函数展开法,利用这一方法求得了非线性发展方程的丰富的Jacobi椭圆函数双周期解.当模数m→0或1时,这些解退化为相应的三角函数解或孤立波解和冲击波解.
关键词:
非线性发展方程
Jacobi椭圆函数
双周期解
行波解 相似文献
16.
R. B. Abbott 《Zeitschrift fur Physik C Particles and Fields》1982,15(1):51-59
A new family of elliptic solutions in the general charge sector of ?P n-1 model is proposed. Forn=2 these solutions interpolate between merons and arbitrary instantons; forn≧3 the situation is less clear. Various properties are investigated, both in Euclidean and Minkowski space. The solutions are found to interact through a potential rising more slowly than logarithmic. 相似文献
17.
Dmitry Pelinovsky Guido Schneider Robert S. MacKay 《Communications in Mathematical Physics》2008,284(3):803-831
We justify the use of the lattice equation (the discrete nonlinear Schrödinger equation) for the tight-binding approximation of stationary localized solutions in the context of a continuous nonlinear elliptic problem with a periodic potential. We rely on properties of the Floquet band-gap spectrum and the Fourier–Bloch decomposition for a linear Schrödinger operator with a periodic potential. Solutions of the nonlinear elliptic problem are represented in terms of Wannier functions and the problem is reduced, using elliptic theory, to a set of nonlinear algebraic equations solvable with the Implicit Function Theorem. Our analysis is developed for a class of piecewise-constant periodic potentials with disjoint spectral bands, which reduce, in a singular limit, to a periodic sequence of infinite walls of a non-zero width. The discrete nonlinear Schrödinger equation is applied to classify localized solutions of the Gross–Pitaevskii equation with a periodic potential. 相似文献
18.
Several nonlinear systems such as the Korteweg-de Vries (KdV) and modified KdV equations and lambda phi(4) theory possess periodic traveling wave solutions involving Jacobi elliptic functions. We show that suitable linear combinations of these known periodic solutions yield many additional solutions with different periods and velocities. This linear superposition procedure works by virtue of some remarkable new identities involving elliptic functions. 相似文献
19.
Applications of Jacobi Elliptic Function Expansion Method for Nonlinear Differential-Difference Equations 总被引:1,自引:0,他引:1
The Jacobi elliptic function expansion method is extended to derive the
explicit periodic wave solutions for nonlinear differential-difference equations. Three well-known examples are
chosen to illustrate the application of the Jacobi elliptic function expansion method. As a result, three types of periodic wave solutions including Jacobi elliptic sine function, Jacobi
elliptic cosine function and the third elliptic function solutions
are obtained. It is shown that the shock wave solutions and
solitary wave solutions can be obtained at their limit condition. 相似文献