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1.
YANG Chun-Nuan HE Jin-Chun HUANG Nian-Ning 《理论物理通讯》2008,50(12):1375-1380
Using the integral representation of the Jost solution, we deduce some conditions as the kernel function N(x, y, t) if the Jost solution satisfies the two Lax equations. Then we verify the multi-soliton solution of NLS equation with non-vanishing boundary conditions if we prove that these conditions can be demonstrated by the GLM equation, which determines the kernel function N (x, y, t) in according to the inverse scattering method. 相似文献
2.
Demonstration of Inverse Scattering Transform for DNLS Equation 总被引:1,自引:0,他引:1
YANG Chun-Nuan YU Jia-Lu WANG Qu-Quan HUANG Nian-Ning 《理论物理通讯》2007,48(2):299-303
Since the Jost solutions of the DNLS equation does not tend to the free Jost solutioins as |λ|→∞, the usual inverse scattering transform (IST) must be revised. Beside the Kaup and Newell's approach, we propose a simple revision in constructing the equations of IST, where the usual Zakharov-Shabat kern is revised by multiplying λ^-2 or λ^-1. To justify the revision we show that the Jost solutions obtained do satisfy the pair of compatibility equations. 相似文献
3.
Since the Jost solutions of the DNLS equation does not tend to the free Jost solutioins as |λ| →∞, the usual inverse scattering transform (IST) must be revised. Beside the Kaup and Newell's approach, we propose a simple revision in constructing the equations of IST, where the usual Zakharov-Shabat kern is revised by multiplying λ-2 or λ-1. To justify the revision we show that the Jost solutions obtained do satisfy the pair of compatibility equations. 相似文献
4.
HE Jing-Song CHEN Shi-Rong 《理论物理通讯》2005,44(2):321-325
Hamiltonian formalism of the mKdV equation with non-vanishing boundary value is re-examined by a revised form of the standard procedure. It is known that the previous papers did not give the final results and involved some questionable points [T.C. Au Yeung and P.C.W. Fung, J. Phys. A 21 (1988) 3575]. In this note, simple results are obtained in terms of an affine parameter and a Galileo transformation is introduced to ensure the results compatible with those derived from the inverse scattering transform. 相似文献
5.
HE Jing-Song CHEN Shi-Rong 《理论物理通讯》2005,44(8)
Hamiltonian formalism of the mKdV equation with non-vanishing boundary valueis re-examined by a revised form of the standard procedure. It is known that the previous papers did not give the final results and involved some questionable points [T.C. Au Yeung and P.C.W. Fung, J. Phys. A 21 (1988) 3575]. In this note, simple results are obtained in terms of an affine parameter and a Galileo transformation is introduced to ensure the results compatible with those derived from the inverse scattering transform. 相似文献
6.
N-soliton solutions of the hierarchy of non-isospectral mKdV equation with self-consistent sources and the hierarchy of non-isospectral sine-Gordon equation with self-consistent sources are obtained via the inverse scattering transform. 相似文献
7.
N-soliton solutions of the hierarchy of non-isospectral mKdV equation with self-consistent sources and the hierarchy of non-isospectral sine-Gordon equation with self-consistent sources are obtained via the inverse scattering transform. 相似文献
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9.
LI Cun YANG Bai-Feng CAI Hao HUANG Nian-Ning 《理论物理通讯》2006,46(2):244-248
One of the basic problems about the inverse scattering transform for solving a completely integrable nonlinear evolutions equation is to demonstrate that the Jost solutions obtained from the inverse scattering equations of Cauchy integral satisfy the Lax equations. Such a basic problem still exists in the procedure of deriving the dark soliton solutions of the NLS equation in normal dispersion with non-vanishing boundary conditions through the inverse scattering transform. In this paper, a pair of Jost solutions with same analytic properties are composed to be a 2 × 2 matrix and then another pair are introduced to be its right inverse confirmed by the Liouville theorem. As they are both 2 × 2 matrices, the right inverse should be the left inverse too, based upon which it is not difficult to show that these Jost solutions satisfy both the first and second Lax equations. As a result of compatibility condition, the dark soliton solutions definitely satisfy the NLS equation in normal dispersion with non-vanishing boundary conditions. 相似文献
10.
Cun Li Tian Yan Hao Cai Bai-Feng Yang Nian-Ning Huang 《International Journal of Theoretical Physics》2006,45(12):2388-2395
The perturbation theory for the Landau-Lifschitz equation for isotropic chain with correction, which is based on the inverse scattering transform (IST), is developed to treat Landau-Lifschitz equation for a spin chain with axis asymmetry. The time-evolution equation of parameters and a formula for the first-order correction is given by treating the equation with axis symmetry as a perturbation to the isotropic equation.
PACS numbers 05.45.Yv, 42.65.-k, 42.50.Md.Supported by the National Science Foundation of China under Grant NO. 10474076 and No. 10375041. 相似文献
11.
A new direct approach based on the separation of variables for soliton perturbations is developed. With the aid of this approach, the effects of perturbation on a soliton of nonlinear Schrödinger (NLS) equation is obtained. In comparison with other direct methods,our approach is very concise and easy to be understood. Besides, no more approximation is employed except for the linearization of the perturbed NLS equation. 相似文献
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13.
Inverse Scattering Transform in Squared Spectral Parameter for DNLS Equation under Vanishing Boundary Conditions 下载免费PDF全文
After a transformation, the inverse scattering transform for the derivative nonlinear Schr6dinger (DNLS) equation is developed in terms of squared spectral parameter. Following this approach, we obtain the orthogonality and completeness relations of free Jost solutions, which is impossibly constructed with usual spectral parameter in the previous works. With the help these relations, the Zakharov-Shabat equations as well as Marchenko equations of IST are derived in the standard way. 相似文献
14.
We study the direct spectral transform for the heat equation associated with the Kadomtsev-Petviashvili. We show that, for real nonsingular exponentially decaying-at-infinity potential, the directproblem is nonsingular for arbitrarily large potentials. Earlier, thisstatement was proved only for potentials satisfying the small normassumption. 相似文献
15.
The unstable nonlinear Schrodinger (NLS) equation is solved by the inverse scattering transform. Based on the constructed Zakharov-Shabat equation, it is shown that the soliton solution of the unstable NLS equation can be known from the soliton solution of the usual NLS equation by simply exchanging the tariables. The explicit N-soliton solution and the position shifts due to the collision are thus calculated. 相似文献
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17.
The Peregrine breather of order eleven(P_(11) breather) solution to the focusing one-dimensional nonlinear Schrdinger equation(NLS) is explicitly constructed here. Deformations of the Peregrine breather of order 11 with 20 real parameters solutions to the NLS equation are also given: when all parameters are equal to 0 we recover the famous P_(11) breather. We obtain new families of quasi-rational solutions to the NLS equation in terms of explicit quotients of polynomials of degree 132 in x and t by a product of an exponential depending on t. We study these solutions by giving patterns of their modulus in the(x; t) plane, in function of the different parameters. 相似文献
18.
Nikolay K. Vitanov Zlatinka I. Dimitrova Kaloyan N. Vitanov 《Entropy (Basel, Switzerland)》2021,23(1)
The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of to solution for arbitrary finite values of . Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM. 相似文献
19.
生物组织、土壤、水等媒质的电特性是频率相关的(称为色散媒质),常利用单极德拜(Debye)模型描述.为重建这一类媒质的色散特性,基于泛函分析和变分法,提出一种三维(3-D)时域电磁(EM)逆散射技术,主要流程为:①根据最小二乘准则,转化逆散射问题为约束最小化问题;②应用罚函数法,转化约束最小化问题为无约束最小化问题;③通过变分计算,解析导出梯度(Fréchet导数)表达式;④利用梯度法求解.此外,引入一阶吉洪诺夫(Tikhonov)正则化以应对逆问题的病态特性和噪声影响.数值应用中,将提出的目的 应用到一个简单的三维癌变乳房模型,借助PRP共轭梯度(CG)算法和时域有限差分(FDTD)法,仿真结果初步证实本文目的 的可行性、有效性和鲁棒性. 相似文献
20.
ZHANG Da-Jun WU Hua 《理论物理通讯》2008,49(4):809-814
This paper investigates in detail the dynamics of the modified KdV equation with self-consistent sources, including characteristics of one-soliton, scattering conditions and phase shifts of two solitons, degenerate case of two solitons and "ghost" solitons, etc. Co-moving coordinate frames are employed in asymptotic analysis. 相似文献