Liming Ling, Q. P. Liu
In this paper, we consider the two component derivative nonlinear Schrödinger equation and present a simple Darboux transformation for it. By iterating this Darboux transformation, we construct a compact representation for the $N-$soliton solutions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We consider Darboux transformations for the derivative nonlinear Schrödinger equation. A new theorem for Darboux transformations of operators with no derivative term are presented and proved. The solution is expressed in quasideterminant forms. Additionally, the parabolic and soliton solutions of the derivative nonlinear Schrödinger equation are given as explicit examples.
In this paper, we construct a Darboux transformation (DT) of the (2+1)-dimensional Schrödinger-Maxwell-Bloch equation (SMBE) which is integrable by the Inverse Scattering Method. Using this DT, the one-soliton solution and periodic solution are obtained from the "seed" solutions.
Darboux transformations for 5-point and 7-point self-adjoint schemes and an integrable discretization of the 2D Schrodinger operator
本文首先研究具有达布变换的差分格式，这些差分格式可以看作是椭圆型偏微分方程的自然离散。特别地，我们构造了一般的具有5个和7个邻点的自伴格式的达布变换。我们还介绍了一个杰出的离散化的二维稳态薛定谔方程，描述了一个5点差分格式涉及两个潜在的，其中承认一个达布变换。
Periodic energy switching of bright solitons in mixed coupled nonlinear Schr{ö}dinger equations with linear self and cross coupling terms
通过确定一个变换将相应的方程变换为可积的混合2-CNLS方程，得到了具有线性自耦合和交叉耦合项的混合2-耦合非线性Schr{<$}dinger（CNLS）方程的亮孤子解.对亮孤子碰撞动力学的研究表明，由于耦合项的存在，存在周期性的能量开关。这种周期性的能量开关可以通过混合2-CNLS系统中产生的亮孤子的新型形状变化碰撞来控制，其特征在于强度重新分布、振幅相关相移和相对分离距离。我们还指出，该系统表现出大的周期性强度切换，即使很小的线性自耦合强度。
A nonlocal derivative nonlinear Schrodinger equation is introduced. By constructing its basic Darboux transformations of degrees one and two, the explicit expressions of new solutions are derived from seed solutions by Darboux transformation of degree 2n. Usually the derived solutions of this nonlocal equation may have singularities. However, by suitable choice of eigenvalues and the parameters describing the ratio of the two entries of the solutions of the Lax pair, global bounded solutions of the nonlocal derivative nonlinear Schrodinger equation are obtained from zero seed solution by a Dar…
In this paper, we construct a generalized Darboux transformation for nonlinear Schrödinger equation. The associated $N$-fold Darboux transformation is given both in terms of a summation formula and in terms of determinants. As applications, we obtain compact representations for the $N$-th order rogue wave solutions of the focusing nonlinear Schrödinger equation and Hirota equation. In particular, the dynamics of the general third order rogue wave is discussed and shown to exhibit interesting structure.
We present a brief discussion on the nonlinear Schr{ö}dinger equation for modeling the propagation of the deep-water wavetrains and a discussion on its doubly-localized breather solutions that can be connected to the sudden formation of extreme waves, also known as rogue waves or freak waves.
In this paper, we obtain a uniform Darboux transformation for multi-component coupled NLS equations, which can be reduced to all previous presented Darboux transformation. As a direct application, we derive the single dark soliton and multi-dark soliton solutions for multi-component coupled NLS with defocusing case and mixed focusing and defocusing case. Some exact single and two-dark solitons of three-component NLS equation are shown by plotting the picture.
Shape changing (intensity redistribution) collisions of solitons in mixed coupled nonlinear Schr{ö}dinger equations
在可积的$N$ -耦合非线性薛定谔（CNLS）方程中，发现了一类新的形状变化（强度重新分布）碰撞，该碰撞具有潜在的信号放大应用价值.利用Hirota的双线性化方法得到了N=2情形的孤子解。混合符号CNLS方程的特点是孤子解既可以是奇异的，也可以是正则的。虽然一般的孤子解承认奇异性，我们提出的参数条件，非奇异孤子传播可以发生。同时给出了多孤子解，并将所得结果推广到任意$N$的多分量情形。在这种情况下，孤子碰撞的一个吸引人的特点是，所有的孤子分量可以同时增强其振幅，这可能导致一种新的放大过程中没有感生噪声。
Perturbation theory for the modified nonlinear Schr{ö}dinger solitons
基于Riemann-Hilbert问题，建立了描述飞秒光脉冲在非线性单模光纤中传输的修正非线性薛定谔方程的微扰理论。详细分析了微扰诱导孤子参数演化的绝热近似。线性微扰和拉曼增益被认为是作为例子。
It is shown that sufficiently large periodic modulations in the coefficients of a nonlinear Schr{ö}dinger equation can drastically impact the spatial shape of the Peregrine soliton solutions: they can develop multiple compression points of the same amplitude, rather than only a single one, as in the spatially homogeneous focusing nonlinear Schr{ö}dinger equation. The additional compression points are generated in pairs forming a comb-like structure. The number of additional pairs depends on the amplitude of the modulation but not on its wavelength, which controls their separation distance. The…
Non-linear Schr$\ddot{o}$dinger equation with time-dependent balanced loss-gain and space-time modulated non-linear interaction
本研究针对含平衡损耗-增益、线性耦合与时空调制非线性作用的一维矢量非线性薛定谔方程，通过非幺正变换与坐标变换映射为可解方程，结合超对称量子力学方法构造了多类势场下的精确局域非线性模与奇异相位解。
Darboux transformations and related non-Abelian integrable differential-difference systems of the derivative nonlinear Schrödinger type
本研究针对7种具Lax表示的非阿贝尔导数非线性Schrödinger方程，构建相容的线性与二次Darboux矩阵，推广了非阿贝尔可积模型，并借助拟行列式得到高次Darboux矩阵的分解条件。
Bäcklund and Darboux transformations for the nonstationary Schrödinger equation
研究了利用$n$递归贝克隆变换构造的非定常Schr dinger算子的位势.介绍了Jost解的相应达布变换。我们表明，这些解决方案服从修改后的积分方程，并提出其解析性质。产生的光谱数据的转换。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。