共查询到19条相似文献,搜索用时 153 毫秒
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利用分离变量法,研究了(2+1)维非线性薛定谔(NLS)方程的局域结构.由于在B?cklund变换和变量分离步骤中引入了作为种子解的任意函数,得到了NLS方程丰富的局域结构.合适地选择任意函数,局域解可以是dromion,环孤子,呼吸子和瞬子.dromion解不仅可以存在于直线孤子的交叉点上,也可以存在于曲线孤子的最近邻点上.呼吸子在幅度和形状上都进行了呼吸
关键词:
非线性薛定谔方程
分离变量法
孤子结构 相似文献
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用分离变量法研究了新(2+1)维非线性演化方程的相干孤子结构.由于Bcklund变换和变量分离步骤中引入了作为种子解的任意函数,得到了新(2+1)维非线性演化方程丰富的孤子解.合适地选择任意函数,孤子解可以是solitoffs,dromions,dromion格子,呼吸子和瞬子.呼吸子不仅在幅度、形状,各峰间距离,甚至在峰的数目上都进行了呼吸.
关键词:
新(2+1)维非线性演化方程
分离变量法
孤子结构 相似文献
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借助Mathematica软件,在Bcklund变换的基础上采用多线性变量分离(MLVS)方法,得到了(2+1)维修正Veselov-Novikov系统的一个含低维任意函数的新的精确解.选取合适的多值函数,构造出新型的折叠子,对其进行了分类并且研究了各种类型的二折叠子之间的完全弹性碰撞.另外还给出了折叠子与隐形折叠子的相互作用.最后把MLVS方法推广到一个新的(1+1)维非线性系统.
关键词:
修正Veselov-Novikov系统
折叠子
弹性碰撞
变量分离 相似文献
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借助于Painlev Bcklund变换和多线性变量分离方法, 求得了(2+1)维非线性Boiti Leon Pempinelle系统的一般变量分离解.根据得到的一般解, 可以构建出丰富的局域相干结构, 如峰状孤子、紧致子等. 得到了两种新的局域结构——钟状圈孤子和峰状圈孤子, 并简要讨论了这两种圈孤子的一些特殊演化性质.
关键词:
Boiti Leon Pempinelle系统
多线性变量分离法
钟状圈孤子
峰状圈孤子 相似文献
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引进一类广义色散Camassa-Holm模型,对其做奇异性分析.通过改进的WTC-Kruskal算法,证明该模型在Painlevé意义下可积,得到了它的一组Painlevé-Bcklund系统和Bcklund变换.应用Maple进行代数运算,得到了丰富的规则(regular)孤子和一类奇异(singular)孤子,扭结(kink)孤子,紧孤子(compacton)和反紧孤子(anti-compacton).特别地,推导出一类在扭结孤子的中间区域包含有一列周期尖点(cuspon)波的奇异结构.在这些规则的孤子系统的基础上,对可积广义系统应用Bcklund变换,得到三类奇异孤子,分别是具有驼峰结构的周期爆破波,具有爆破波结构的扭结孤子和紧孤子.
关键词:
广义Camassa-Holm 模型
周期尖点波
紧孤子
周期爆破波 相似文献
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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
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We study the localized coherent structures ofa generally nonintegrable (2 1 )-dimensional KdV equation via a variable separation approach. In a special integrable case, the entrance of some arbitrary functions leads to abundant coherent structures. However, in the general nonintegrable case, an additional condition has to be introduced for these arbitrary functions. Although the additional condition has been introduced into the solutions of the nonintegrable KdV equation, there still exist many interesting solitary wave structures. Especially, the nonintegrable KdV equation possesses the breather-like localized excitations, and the similar static ring soliton solutions as in the integrable case. Furthermor,in the integrable case, the interaction between two travelling ring solitons is elastic, while in the nonintegrable case we cannot find even the single travelling ring soliton solution. 相似文献
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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
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Considering that folded phenomena are rather universal in nature and some arbitrary functions can be included in the exact excitations of many (2+1)-dimensional soliton systems, we use adequate multivalued functions to construct folded solitary structures in multi-dimensions. Based on some interesting variable separation results in the literature, a common formula with arbitrary functions has been derived for suitable physical quantities of some significant (2+1)-dimensional soliton systems like the generalized Ablowitz-Kaup-Newell-Segur (GAKNS) model, the generalized Nizhnik-Novikov-Veselov (GNNV) system and the new (2+1)-dimensional long dispersive wave (NLDW) system. Then a new special type of two-dimensional solitary wave structure, i.e. the folded solitary wave and foldon, is obtained. The novel structure exhibits interesting features not found in the single valued solitary excitations. 相似文献
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By means of the Weiss–Tabor–Carnevale (WTC) truncation method and the general variable separation approach (GVSA), analytical investigation of the integrable (2+1)-dimensional higher-order Broer–Kaup (HBK) system shows, due to the possibility of selecting three arbitrary func.tions, the existence of interacting coherent excitations such as dromions, solitons, periodic solitons, etc. The interaction between some of the localized solutions are elastic because they pass through each other and preserve their shapes and velocities, the only change being the phase shift. However, as for some soliton models, completely non-elastic interactions have been found in this model. These non-elastic interactions are characterized by the fact that, at a specific time, one soliton may fission to two or more solitons; or on the contrary, two or more solitons will fuse to one soliton. 相似文献
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Coherent soliton structures of the (2+1)-dimensional long-wave-short-wave resonance interaction equation 下载免费PDF全文
The variable separation approach is used to find exact solutions of the (2+1)-dimensional long-wave-short-wave resonance interaction equation. The abundance of the coherent soliton structures of this model is introduced by the entrance of an arbitrary function of the seed solutions. For some special selections of the arbitrary function, it is shown that the coherent soliton structures may be dromions, solitoffs, etc. 相似文献
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For a higher-dimensional integrable nonlinear dynamical system, there are abundant coherent soliton excitations. With the aid of an improved projective Riccati equation approach, the paper obtains several types of exact solutions to the (2 1)-dimensional dispersive long-wave equation, including multiple-soliton solutions, periodic soliton solutions, and Weierstrass function solutions. From these solutions, apart from several multisoliton excitations, we derive some novel features of wave structures by introducing some types of lower-dimensional patterns. 相似文献
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Considering that the multi-valued (folded) localized excitations may appear in many (2 1)-dimensional soliton equations because some arbitrary functions can be included in the exact solutions, we use some special types of muliti-valued functions to construct folded solitrary waves and foldons in the (2 1)-dimensional Broer-Kaup equation.These folded excitations are invesigated both analytically and graphically in an alternative way. 相似文献
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XU Chang-Zhi 《理论物理通讯》2006,46(9)
Variable separation approach is introduced to solve the (2 1)-dimensional KdV equation. A series of variable separation solutions is derived with arbitrary functions in system. We present a new soliton excitation model (24). Based on this excitation, new soliton structures such as the multi-lump soliton and periodic soliton are revealed by selecting the arbitrary function appropriately. 相似文献
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Variable separation solutions and new solitary wave structures to the (l+l)-dimensional Ito system 下载免费PDF全文
A variable separation approach is proposed and extended to the (1+1)-dimensional physics system. The variable separation solution of (1-F1)-dimensional Ito system is obtained. Some special types of solutions such as non-propagating solitary wave solution, propagating solitary wave solution and looped soliton solution are found by selecting the arbitrary function appropriately. 相似文献