共查询到18条相似文献,搜索用时 250 毫秒
1.
从(2+1)维双线性形式的非局域Bussinesq(NLBQ)方程和KP方程的隐线孤子解出发,可以找到与某种势所相应的各方向都指数衰减的dromion解.利用图形分析的方法,对这些dromion之间的相互作用进行了详细的研究.发现这两种模型中的dromion间的相互作用只引起位相漂移,不引起形状和速度的变化,也不引起旋转.即dromion间的相互作用是弹性的,没有能量、动量和角动量的交换.
关键词: 相似文献
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利用双线性方法给出了2+1维Sawaka-Kotera(SK)方程的N孤子解.将N孤子解中的实参数扩大到复数范围,得到了该方程的呼吸子解,描述线孤子和y周期孤子相互作用的解和两个y周期孤子相互作用的解.从解析和几何两个角度探讨了两个y周期孤子的相互作用.相互作用性质和耦合系数有关.对于SK方程,耦合系数的取值只允许方程中存在弹性的排斥相互作用.
关键词:
y周期孤子相互作用
SK方程
双线性方法 相似文献
3.
利用分离变量法得到了2+1维Nizhnik-Novikov-Veselov方程包含三个任意函数的精确解.合 适地选择任意函数,该精确解可以是描述所有方向指数局域的dromion相互作用,三个方向 指数局域的‘Solitoff’和dromion相互作用以及线孤子和y周期孤子相互作用的解.对dromi on相互作用从解析和几何两个角度进行了详细地探讨,揭示了一些新的相互作用规律.
关键词:
dromions相互作用
NNV方程
分离变量法 相似文献
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可积系统研究是物理和数学等学科的重要研究课题.然而,通常的可积系统研究往往被限制在(1+1)维和(2+1)维,其原因是高维可积系统极其稀少.最近,我们发现利用形变术可以从低维可积系统导出大量的高维可积系统.本文利用形变术,将(1+1)维的Kaup-Newell(KN)系统推广到(4+1)维系统.新系统除了包含原来的(1+1)维的KN系统外,还包含三种(1+1)维KN系统的互反形式.模型也包含了许多新的(D+1)维(D≤3)的互反型可积系统.(4+1)维互反型KN系统的Lax可积性和对称可积性也被证明.新的互反型高维KN系统的求解非常困难.本文仅研究(2+1)维互反型导数非线性薛定谔方程的行波解,并给出薛定谔方程孤子解的隐函数表达式. 相似文献
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利用推广的齐次平衡方法,首先将(2+1)维Broer-Kaup方程线性化,然后构造出丰富的广义孤子解,包括单孤子解,单曲线孤子解,单dromion解,多dromion解。此方法直接而简单,可推广应用一大类(2+1)维非线性可积方程。 相似文献
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研究(1+1)维广义的浅水波方程的变量分离解和孤子激发模式. 该方程包括两种完全可积(IST可积)的特殊情况,分别为AKNS方程和Hirota-Satsuma方程. 首先把基于Bcklund变换的变量分离(BT-VS)方法推广到该方程,得到了含有低维任意函数的变量分离解. 对于可积的情况,含有一个空间任意函数和一个时间任意函数,而对于不可积的情况,仅含有一个时间任意函数,其空间函数需要满足附加条件. 另外,对于得到的(1+1)维普适公式,选取合适的函数,构造了丰富的孤子激发模式,包括单孤子,正-反孤子,孤子膨胀,类呼吸子,类瞬子等等. 最后,对BT-VS方法作一些讨论.
关键词:
浅水波方程
Bcklund变换
变量分离
孤子 相似文献
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Starting from n line soliton solutions of an integrable (2+1)-dimensional sine-Gordon system, one can find a dromion solution which is localized in all directions for a suitable potential. The dromion structures for a special (2+1)-dimensional sine-Gordon equation are studied in detail. The interactions among dromions are not elastic. In addition to a phase shift, the "shape" and the velocity of these dromions may also be changed after interaction. 相似文献
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Some new structures and interactions of solitons for the (2+1)-dimensional Nizhnik-Novikov-Veselov equation are revealed with the help of the idea of the bilinear method and variable
separation approach. The solutions to describe the interactions between two dromions, between a line soliton and a y-periodic soliton, and between two y-periodic solitons are included in our
results. Detailed behaviors of interaction are illustrated both
analytically and in graphically. Our analysis shows that the
interaction properties between two solitons are related to the
form of interaction constant. The form of interaction constant and
the dispersion relationship are related to the form of the seed
solution {u0, v0, w0} in Bäcklund transformation. 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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From the variable separation solution and by selecting appropriate functions, a new class of localized coherent structures consisting of solitons in various types are found in the (2 1)-dimensional long-wave-short-wave resonance interaction equation. The completely elastic and non-elastic interactive behavior between the dromion and compacton, dromion and peakon, as well as between peakon and compacton are investigated. The novel features exhibited by these new structures are revealed for the first time. 相似文献
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ZHANGJie-Fang: MENGJian-Ping HUANGWen-Hua 《理论物理通讯》2004,42(2):161-170
From the variable separation solution and by selecting appropriate functions, a new class of localized coherent structures consisting of solitons in various types are found in the (2 1)-dimensional long-wave-short-wave resonance interaction equation. The completely elastic and non-elastic interactive behavior between the dromion and compacton, dromion and peakon, as well as between peakon and compacton are investigated. The novel features exhibited by these new structures are revealed for the first time. 相似文献
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Zhang Jiefang 《International Journal of Theoretical Physics》1999,38(8):2253-2258
Hirota's bilinear form of the (2 +1)-dimensional breaking-soliton equations introduced byBogyovlenskii is deduced in a straightforward manner andused to construct wave-type solutions for the fieldvariables. The peculiar localization behavior of thesystem by the generating dromion for the composite fieldvariable qr is also brought out and is generalized to(1, N, 1) dromions. 相似文献
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RUAN Hang-Yu 《理论物理通讯》2005,43(1):31-38
A variable separation approach is used to obtain exact solutions
of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov
equation. Two of these exact solutions are analyzed to study the
interaction between a line soliton and a y-periodic soliton (i.e. the array of the localized structure in the y direction, which propagates in the x direction) and between two dromions. The
interactions between a line soliton and a y-periodic soliton are
classified into several types according to the phase shifts due to
collision. There are two types of singular interactions. One is
the resonant interaction that generates one line soliton while the
other is the extremely repulsive or long-range interaction where
two solitons interchange each other infinitely apart. Some new
phenomena of interaction between two dromions are also reported in
this paper, and detailed behaviors of interactions are illustrated both
analytically and graphically. 相似文献
18.
ZHANGJie-Fang 《理论物理通讯》2001,35(3):267-270
We derive the generalized dromions of the new(2 1)-dimensional nonlinear evolution equation by the arbitrary function presented in the bilinearized linear equations.The rich soliton and dromion structures for this system are released. 相似文献