共查询到20条相似文献,搜索用时 15 毫秒
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ZHANGJin-liang WANGMing-liang FANGZong-de 《原子与分子物理学报》2004,21(1):78-82
By using the extended F-expansion method,the exact solutions,including periodic wave solutions expressed by Jaeobi elliptic functions,for (2 1)-dimensional nonlinear Schroedinger equation are derived.In the limit cases,the solitary wave solutions and the other type of traveling wave solutions for the system are obtained. 相似文献
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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
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General Solution and Fractal Localized Structures for the (2+1)—Dimensional Generalized Ablowitz—Kaup—Newell—Segur System 总被引:4,自引:0,他引:4 下载免费PDF全文
Using the standard truncated Painleve expansions,we derive a quite general solution of the (2 1)-dimensional generalized Ablowitz-Kaup-Newell-Segur system.Except for the usual localized solutions,such as dromions,lumps,ring soliton solutions,etc,some special localized excitations with fractal behaviour i.e.the fractal dromion and fractal lump excitations,are obtained by some types of lower-dimensional fractal patterns. 相似文献
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Peakon and Foldon Excitations in a (2+1)—Dimensional Breaking Soliton System 总被引:7,自引:0,他引:7 下载免费PDF全文
《中国物理快报》2003,20(6):783-786
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We show that, due to the nonlinear coupling between a wavepacket superposed by short-wavelength collective modes and a long-wavelength mean field generated by the self-interaction of the wavepacket, the (2 1)-dimensional envelope solitons decaying in all spatial directions, i.e., dromions, are possible nonlinear excitations in a disk-shaped Bose-Einstein condensate with a repulsive interatomic interaction. 相似文献
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New exact excitations and soliton fission and fusion for the (2+1)-dimensional Broer-Kaup-Kupershmidt system 总被引:3,自引:0,他引:3 下载免费PDF全文
With the help of an extended mapping approach, a series of new types of exact excitations with two arbitrary functions of the (2 1)-dimensional Broer-Kaup-Kupershmidt (BKK) system is derived. Based on the derived solitary wave excitation, some specific soliton fission and fusion solutions of the higher-dimensional BKK system are also obtained. 相似文献
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In this paper, a generalized Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy in inhomogeneities of media described by variable coefficients is investigated, which includes some important nonlinear evolution equations as special cases, for example, the celebrated Korteweg–de Vries equation modeling waves on shallow water surfaces. To be specific, the known AKNS spectral problem and its time evolution equation are first generalized by embedding a finite number of differentiable and time-dependent functions. Starting from the generalized AKNS spectral problem and its generalized time evolution equation, a generalized AKNS hierarchy with variable coefficients is then derived. Furthermore, based on a systematic analysis on the time dependence of related scattering data of the generalized AKNS spectral problem, exact solutions of the generalized AKNS hierarchy are formulated through the inverse scattering transform method. In the case of reflectionless potentials, the obtained exact solutions are reduced to n-soliton solutions. It is graphically shown that the dynamical evolutions of such soliton solutions are influenced by not only the time-dependent coefficients but also the related scattering data in the process of propagations. 相似文献
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With a projective equation and a linear variable separation method, this paper derives new families of variable separation solutions (including solitory wave solutions, periodic wave solutions, and rational function solutions) with arbitrary functions for (2+1)-dimensional generalized Breor-Kaup (GBK) system. Based on the derived solitary wave excitation, it obtains fusion and fission solitons. 相似文献
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New Solitary Solutions of (2+1)-Dimensional Variable Coefficient Nonlinear Schrodinger Equation with an External Potential 下载免费PDF全文
By a series of transformations, the (2+1)-dimensional variable coefficient nonlinear Schr?dinger equation can turn to the Klein-Gordon equation. Many new double travelling wave solutions of the Klein-Gordon equation are obtained. Thus, the new solitary solutions of the variable coefficient nonlinear Schr?inger equation with an external potential can be found. 相似文献
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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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A broad general variable separation solution with two arbitrary lower-dimensional functions of the (2+1)-dimensional Broer–Kaup (BK) equations was derived by means of a projective equation method and a variable separation hypothesis. Based on the derived variable separation excitation, some new special types of localized solutions such as oscillating solitons, instanton-like and cross-like fractal structures are revealed by selecting appropriate functions of the general variable separation solution. 相似文献
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In this paper,an improved projective approach is used to obtain the variable separation solutions with two arbitrary functions of the (2+1)-dimensional Broek-Kaup equation with variable coefficients (VCBK). Based on the derived solitary wave solution and using a known chaotic system,some novel chaotic solutions are investigated. 相似文献
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从(1+2)维非局域非线性薛定谔方程出发, 通过坐标变换得到了旋转坐标系下的非局域非线性薛定谔方程. 假设响应函数为高斯型, 用虚时间法数值求解了旋转坐标系下的非局域非线性薛定谔方程的静态孤子解, 迭代出了不同非局域程度条件下的静态椭圆孤子数值解. 最后采用分步傅里叶算法, 以迭代的孤子解作为初始输入波形, 模拟了在不同的非局域程度条件下, (1+2)维椭圆空间光孤子的旋转传输特性. 强非局域时, 椭圆光孤子的长轴方向和短轴方向波形都是高斯型, 其他的非局域程度下, 不是高斯型. 由此表明:(1+2)维椭圆光孤子对非局域程度依赖性很强. 旋转角速度和功率均与非局域程度以及孤子的椭圆度有关. 相似文献
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With a new projective equation, a series of solutions of the (2-J-1)-dimensional dispersive long-water wave system (LWW) is derived. Based on the derived solitary wave solution, we obtain some special fractal localized structures and chaotic patterns. 相似文献