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1.
In this paper,the variable separation approach is used to obtain localized coherent structures of the (2 1)-dimensional generalized Davey-Stewarson equations:iqt 1/2(qxx=qyy) (R S)q=0,Rx=-σ/2|q|y^2,Sy=-σ/2|q|2/x.Applying a special Baecklund transformation and introducing arbitrary functions of the seed solutions.and abundance of the localized structures of this model is derived,By selceting the arbitrary functions appropriately,some special types of localized excitations such as dromions,dromion lattice,breathers,and instantons are constructed. 相似文献
2.
In this paper, we introduce a new invariant set
˜E0={u:ux=fˊ(x)F(u)+ε [gˊ(x)
-fˊ(x)g(x)]F(u)exp(-∫u(1/F(z))dz), where f and g are some smooth functions of x, ε
is a constant, and F is a smooth function to be determined. The
invariant sets and exact solutions to nonlinear diffusion equation
ut=(D(u)ux)x+Q(x,u)ux+P(x,u), are discussed. It is shown
that there exist several classes of solutions to the equation that
belong to the invariant set
˜E0. 相似文献
3.
By means of the Baecklund transformation, a quite general variable separation solution of the (2 1)-dimensional Maccari systems is derived. In addition to some types of the usual localized excitations such as dromion, lumps, ring soliton and oscillated dromion, breathers solution, fractal-dromion, fractal-lump and chaotic soliton structures can be easily constructed by selecting the arbitrary functions appropriately, a new novel class of coherent localized structures like peakon solution and compacton solution of this new system are found by selecting apfropriate functions. 相似文献
4.
YANZhen-Ya 《理论物理通讯》2001,36(2):135-138
We obtain Backlund transformation and some new kink-like solitary wave solutions for the generalized Burgers equation in (2 1)-dimensional space,ut 1/2(uδy^-1ux)x-uxx=0,by using the extended homogeneous balance method.As is well known,the introduction of the concept of dromions (the exponentially localized solutions in (2 1)-dimensional space)has triggered renewed interest in (2 1)-dimensional soliton systems.The solutions obtained are used to show that the variable ux admits exponentially localized solutions rather than the physical field u(x,y,t) itself.In addition,it is shown that the equation passes Painleve test. 相似文献
5.
6.
By means of the Backlund transformation, a quite general variable separation solution of the (2 1)-dimensional Maccari systems is derived. In addition to some types of the usual localized excitations such as dromion,lumps, ring soliton and oscillated dromion, breathers solution, fractal-dromion, fractal-lump and chaotic soliton structurescan be easily constructed by selecting the arbitrary functions appropriately, a new novel class of coherent localizedstructures like peakon solution and compacton solution of this new system are found by selecting aperopriate functions. 相似文献
7.
The spin-boson model with quadratic coupling is studied using the bosonic numerical renormalization group method.We focus on the dynamical auto-correlation functions C_O(ω), with the operator taken as σ_x, σ_z, and X, respectively. In the weak-coupling regime α α_c, these functions show power law ω-dependence in the small frequency limit, with the powers 1 + 2s, 1 + 2s, and s, respectively. At the critical point α = α_c of the boson-unstable quantum phase transition, the critical exponents y_O of these correlation functions are obtained as yσ_x= yσ_z= 1-2s and yX=-s, respectively. Here s is the bath index and X is the boson displacement operator. Close to the spin flip point, the high frequency peak of Cσ_x(ω) is broadened significantly and the line shape changes qualitatively, showing enhanced dephasing at the spin flip point. 相似文献
8.
In this paper, the variable separation approach is used to obtain localized coherent structures of the (2 1)-dimensional generalized Davey-Stewarson equations: iqt 1/2(qxx qyy) (R S)q = O, Rx=-σ/2|q|2y Sy = -σ/2|q|2/x.Applying a special Backlund transformation and introducing arbitrary functions of the seed solutions, an abundance of the localized structures of this model is derived. By selecting the arbitrary functions appropriately, some special typesof localized excitations such as dromions, dromion lattice, breathers, and instantons are constructed. 相似文献
9.
SHEN Shou-Feng 《理论物理通讯》2006,45(2):236-238
By means of the variable separation method, new exact solutions of some (1+1)-dimensional nonlinear evolution
equations are obtained. Abundant localized excitations can be
found by selecting corresponding arbitrary functions
appropriately. Namely, the new soliton-like localized excitations
and instanton-like localized excitations are presented. 相似文献
10.
Two classes of fractal structures for the (2+1)-dimensional dispersive long wave equation 总被引:1,自引:0,他引:1 下载免费PDF全文
Using the mapping approach via a Riccati equation, a series of variable separation
excitations with three arbitrary functions for the (2+1)-dimensional dispersive long wave (DLW)
equation are derived. In addition to the usual localized coherent soliton excitations like
dromions, rings, peakons and compactions, etc, some new types of excitations
that possess fractal behaviour are obtained by introducing appropriate
lower-dimensional localized patterns and Jacobian elliptic functions. 相似文献
11.
将扩展的Riccati方程映射法推广到了(3+1)维非线性Burgers系统,得到了系统的分离变量解;由于在解中含有一个关于自变量(x,y,z,t)的任意函数,通过对这个任意函数的适当选取,并借助于数学软件Mathematica进行数值模拟,得到了系统的新而丰富的局域激发结构和分形结构.结果表明,扩展的Riccati方程映射法在求解高维非线性系统时,仍然是一种行之有效的方法,并且可以得到比(2+1)维非线性系统更为丰富的局域激发结构.
关键词:
扩展的Riccati方程映射法
(3+1)维非线性Burgers方程
局域激发结构
分形结构 相似文献
12.
By an improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the (2+1)-dimensional Broek--Kaup system is derived. Based on the derived solitary wave solution and by selecting appropriate functions, some novel localized excitations such as instantaneous solitons and fractal solitons are investigated. 相似文献
13.
在(1 1)维非线性动力学系统,人们发现不同的局域激发模式分别存在于不同的非线性系统.可是最近的若干研究表明,在高维非线性动力学系统中,如果选取适当的边值条件或初始条件时,人们可以同时找到若干不同的局域激发模式,如:紧致子、峰孤子、呼吸子和折叠子等.本文的主要目的是寻找(1 1)维非线性耦合Ito系统中的不同的局域激发模式.首先,基于一个特殊的Painlev-éBacklund变换和线性变量分离方法,求得了该系统具有若干任意函数的变量分离严格解.然后,根据得到的变量分离严格解,通过选择严格解中的任意函数,引入恰当的单值分段连续函数和多值局域函数,成功找到了耦合Ito系统若干有实际物理意义的单值和多值局域激发模式,如:峰孤子,紧致子和多圈孤子等. 相似文献
14.
ZHENG Chun-Long 《理论物理通讯》2005,43(6):1061-1067
Using an extended projective method, a new type of variable
separation solution with two arbitrary functions of the
(2+1)-dimensional generalized Broer-Kaup system (GBK) is derived.
Based on the derived variable separation solution, some special
localized coherent soliton excitations with or without elastic
behaviors such as dromions, peakons, and foldons etc. are
revealed by selecting appropriate functions in this paper. 相似文献
15.
In this paper, we introduce
the notion of a (2+1)-dimensional differential equation describing
three-dimensional hyperbolic spaces (3-h.s.). The (2+1)-dimensional coupled nonlinear Schrödinger equation and its
sister equation, the (2+1)-dimensional coupled derivative nonlinear Schrödinger equation, are shown to describe 3-h.s. The (2+1)-dimensional generalized HF model:
St={(1/2i)[S,Sy]+2iσS}x,
σx=-(1/4i)tr(SSxSy), in which S∈[GLC(2)]/[GLC(1)×GLC(1)], provides another example of (2+1)-dimensional differential equations describing 3-h.s. As a direct consequence, the geometric construction of an infinite
number of conservation laws of such equations is illustrated.
Furthermore we display a new infinite number of conservation laws
of the (2+1)-dimensional nonlinear Schrödinger equation and the
(2+1)-dimensional derivative nonlinear Schrödinger equation
by a geometric way. 相似文献
16.
With the help of an extended mapping approach and a linear variable separation method, new families of variable separation solutions with arbitrary functions for the (3+1)-dimensional Burgers system are derived. Based on the derived exact solutions,
some novel and interesting localized coherent excitations such as
embed-solitons are revealed by selecting appropriate boundary
conditions and/or initial qualifications. The time evolutional properties of the novel localized excitation are also briefly investigated. 相似文献
17.
ZHENGChun-Long 《理论物理通讯》2003,40(1):25-32
In this work, we reveal a novel phenomenon that the localized coherent structures of some (2 1)-dimensional physical models possess chaotic and fractal behaviors. To clarify these interesting phenomena, we take the (2 l)-dimensional modified dispersive water-wave system as a concrete example. Starting from a variable separation approach,a general variable separation solution of this system is derived. Besides the stable located coherent soliton excitations like dromions, lumps, rings, peakons, and oscillating soliton excitations, some new excitations with chaotic and fractal behaviors are derived by introducing some types of lower dimensional chaotic and fractal patterns. 相似文献
18.
In this Letter, we show that the new (2+1)-dimensional mKdV equation possesses Painlevé property. Then, starting from the standard truncated Laurent expansion and the direct variable separation approach, a new exact solution with two lower dimensional arbitrary functions is obtained. Some high-dimensional localized excitations of the physical quantity u are constructed. These localized excitations have abundant structures at x-axis and y-axis such as dromions, peakons, loop-solitons, compactons which depend on corresponding functions. 相似文献
19.
SHEN Shou-Feng 《理论物理通讯》2005,44(6):961-963
In this letter, by means of the Lax pair, Darboux transformation, and variable separation approach, a new exact solution of a sixth-order (1+1)-dimensional nonlinear evolution equation, which includes some arbitrary functions, is obtained. Abundant new localized excitations can be found by selecting appropriate functions and they are illustrated both analytically and graphically. 相似文献
20.
Starting with the extended homogeneous balance method and a variable separation approach, a general variable separation solution of the Broer—Kaup system is derived. In addition to the usual localized coherent soliton excitations like dromions, lumps, rings, breathers, instantons, oscillating soliton excitations, peakon and fractal localized solutions, some new types of localized excitations, such as compacton and folded excitations, are obtained by introducing appropriate lower-dimensional piecewise smooth functions and multiple-valued functions, and some interesting novel features of these structures are revealed. 相似文献