Large Amplitude Solitary Waves in a Fluid-Filled Elastic Tube

By using the potential method to a fluid filled elastic tube, we obtained a solitary wave solution. Comparedwith reductive perturbation method, this method can be used for larger amplitude solitary waves. The result is inagreement with that of small amplitude approximation from reductive perturbation method when the amplitude is smallenough.     

Effect of Weakly Transverse Perturbations on Dust Acoustic Solitary Waves with Adiabatic Variation of Dust Charge

By employing the reductive perturbation technique we derived a Kadomtsev-Petviashvili equation forunmagnetized dusty plasmas. It suggests that the nonlinear dust acoustic solitary waves with adiabatic variation of dustcharge are stable even there are some higher order transverse perturbatoins. There are only rarefactive solitary wavesfor this system which has been verified analytically in this paper.     

Large Amplitude Solitary Waves in a Fluid－Filled Elastic Tube

By usign the potential method to a fluid filled elastic tube, we obtained a solitary wave solution.Compared with recluetive perturbation method, this method can be used for larger amplitude solitary waves. The result is in agreement with that of small amplitude approximation from reduetive perturbation method when the amplitude is small enough.     

Effect of Weakly Transverse Perturbations on Dust Acoustic Solitary Waves with Adiabatic Variation of Dust Charge

By employing the reductive perturbation technique we derived a Kadomtsev-Petviashvili equation for unmagnetized dusty plasmas,It suggests that the nonlinear dust acoustic solitary waves with adiabatic variation of dust charge are stable even there are some higher order transverse perturbatoins,There are only rarefactive solitary waves for this system which has been verified analytically in this paper.     

Dark Spatial Solitary Wave Due to Cascaded x(2) Nonlinearity

The formation of the dark spatial solitary wave in cascaded second harmonic generation processes is numerically studied based on the nonlinear-coupled equations. It is shown that the solitary wave exists when the effective three-order nonlinearity induced by cascaded second-order nonlinearity is negative.     

Dark Spatial Solitary Wave Due to Cascaded x^（2） Nonlinearity

The formation of the dark spatial solitary wave in cascaded second harmonic generation processes is numerically studied based on the nonlinear-coupled equations. It is shown that the solitary wave exists when the effective three-order nonlinearity induced by cascaded second-order nonlinearity is negative.     

Effect of adiabatic variation of dust charges on dust acoustic solitary waves in magnetized dusty plasmas

The effect of dust charging and the influence of its adiabatic variation on dust acoustic waves is investigated. By employing the reductive perturbation technique we derived a Zakharov－Kuznetsov (ZK) equation for small amplitude dust acoustic waves. We have analytically verified that there are only rarefactive solitary waves for this system. The instability region for one-dimensional solitary wave under transverse perturbations has also been obtained. The obliquely propagating solitary waves to the z-direction for the ZK equation are given in this paper as well.     

Interaction and resonance phenomena of multi-soliton

As is well known, Korteweg-de Vries equation is a typical one which has planar solitary wave. By considering higher order transverse disturbance to planar solitary waves, we study a Kadomtsev-Petviashvili (KP) equation and find some interesting results. In this letter we investigate the three soliton interaction and their resonance phenomena of KP equation, and theoretically find that the maximum amplitude is 9 times of the initial interacting soliton for three same amplitude solitions. Three arbitrary amplitude solition interaction of KP equation is also studied by numerical simulation, which can also results in resonance phenomena.     

Multi-valued solitary waves in multidimensional soliton systems

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.     

Self-trapped optical beams: Spatial solitons

We present a brief overview of the basic concepts of the theory of spatial optical solitons, including the soliton stability in non-Kerr media, the instability-induced soliton dynamics, and collision of solitary waves in nonintegrable nonlinear models.     

Exact Solitons of a d-Dimensional Discrete Modified KdV Equation

We show by using the real exponential approach that the d-dimensional discrete modified KdV equation has more general exact solitary wave solutions than the known bright soliton and kink solutions. Depending on the values of the parameters, the new solutions can describe both bright and dark solitary waves.     

温度对闭路光伏明空间孤子演化和自偏转的影响 (英文)

通过考虑扩散效应的影响，采用数值方法研究了温度对光伏光折变介质中的明空间孤子演化和自偏转的影响。结果表明，当晶体温度变化时，明孤子可以呈现为稳定态、较大周期的压缩和膨胀态，或塌陷态。同时，明空间孤子中心偏转距离随温度增加而增加，在一个特定温度处达到最大值，之后随温度增加而减小，在高温和低温区域此偏转距离趋于零。孤子的最大偏转距离和对应的特定温度随入射孤子波强度的增加而增加。进一步采用微扰方法研究了明孤子自偏转过程，其结果与数值方法获得的结果一致。     

Formation of solitary structures and envelope solitons in electron acoustic wave in inner magnetosphere plasma with suprathermal ions

The propagation of electron acoustic solitary waves is investigated in magnetized two-temperature electron plasma with supra-thermal ion. By using the reductive perturbation technique, the Korteweg de-Vries (KdV) equation is derived. Later solving this equation, a solitary wave solution has been derived. These are mainly in astrophysical plasmas where changes of local charge density, temperature, and energy of particles produce considerable effects on the plasma system. The effects of supra-thermality, density, and Mach number on solitary structures are studied in detail. The results show that the supra-thermal index (κ) and ion to electron temperature ratio (σ) alters the regime where solitary waves may exist. While studying the solitary profile for different parametric variation some interesting conclusion can be drawn; it is shown that the solitary profile becomes flatter. This can be due to the thermal energy associated with the hot electrons. However, with the increase in ion density with respect to the cold electrons' density, the solitary waves become steeper and sharper. This is due to the comparatively heavier mass of ions. The density of cold electron also increases the solitary structures in a similar manner. The higher the density of cold electrons, sharper will be the profile. The above findings will be helpful in understanding many astrophysical phenomena and data obtained by space missions. For a further study, we keep the investigation of the formation of other kinds of stationary structures like shocks, double layers, etc.     

Stability of Multidimensional Solitary Waves for Cubic-Quintic Nonlinearity

We show analytically that in the presence of cubic and quintic nonlinearities above a certain critical power, multidimensional optical solitary waves could propagate stably in bulk media. To investigate the stability an analytical expression for the solitary-wave fields with an arbitrary transverse dimension is derived through the combined use of Galerkin’s method and self-consistent-field approximation.     

高斯光束孤波演化过程中的自偏转

研究了无耗晶体的扩散效应对高斯光束在光伏光折变晶体中孤波演化特性的影响。结果表明，对于给定的与晶体参量匹配的高斯光束，晶体的扩散效应将造成高斯光束孤波演化的自偏转，而且其自偏转过程与同参量的屏蔽光伏明孤子的自偏转过程具有极其类似的特征。同时发现，高斯光束的波形即光束的横截面对其孤波演化的自偏转影响最大。比较了高斯光束孤波演化的自偏转与明孤波自偏转的理论曲线，结果表明，对于匹配的高斯光束，其自偏转程度与解析计算结果非常接近。     

Study on an extended Boussinesq equation

An extended Boussinesq equation that models weakly nonlinear and weakly dispersive waves on a uniform layer of water is studied in this paper. The results show that the equation is not Painlev\'e-integrable in general. Some particular exact travelling wave solutions are obtained by using a function expansion method. An approximate solitary wave solution with physical significance is obtained by using a perturbation method. We find that the extended Boussinesq equation with a depth parameter of $1/\sqrt 2$ is able to match the Laitone's (1960) second order solitary wave solution of the Euler equations.     

Spin density polarization effects in the presence of Coriolis force on ion acoustic waves in quantum plasma

Ion acoustic solitary waves in a quantum plasma, which is slowly rotating around an axis at an angle θ with the direction of magnetic field, are investigated. Quantum hydrodynamic model is under consideration with the effects of rotations which are included via Coriolis force. Fermions are degenerate and have different spin density states, that is, up and down characterized via parameter α. Linear analysis is performed by applying Fourier transformation to derive dispersion relation. For nonlinear analysis, we apply reductive perturbation method to derive Korteweg de Vries equation (KdV). The effects of variations of Coriolis force, spin polarization, and quantum parameter on characteristics of solitary structure are discussed. These results are applicable to astrophysical and laboratory plasmas.     

Abundant Multisoliton Structure of (3+1)-Dimensional Breaking Soliton Equation

Using the extended homogeneous balance method, we obtained abundant exact solution structures of the (3 1 )-dimensional breaking soliton equation. By means of the leading order term analysis, the nonlinear transformations of the (3t1)-dimensional breaking soliton equation are given first, and then some special types of single solitary wave solutions and the multisoliton solutions are constructed.     

密度矩阵重正化群的异构并行优化

密度矩阵重正化群方法（DMRG）在求解一维强关联格点模型的基态时可以获得较高的精度,在应用于二维或准二维问题时,要达到类似的精度通常需要较大的计算量与存储空间.本文提出一种新的DMRG异构并行策略,可以同时发挥计算机中央处理器（CPU）和图形处理器（GPU）的计算性能.针对最耗时的哈密顿量对角化部分,实现了数据的分布式存储,并且给出了CPU和GPU之间的负载平衡策略.以费米Hubbard模型为例,测试了异构并行程序在不同DMRG保留状态数下的运行表现,并给出了相应的性能基准.应用于4腿梯子时,观测到了高温超导中常见的电荷密度条纹,此时保留状态数达到10⁴,使用的GPU显存小于12 GB.     

New Rational Solutions for Relativistic Discrete Toda Lattice System

In the present work, we examine the soliton excitations in the relativistic Toda lattice model using the rotational expansion method, where the coupling between the lattice sites is varied. For specific choices of the coupling strength we proceed to analyze the nonlinear wave excitations arising in the model which are found to be dark, singular and periodic solitary wave profiles. These solitary wave profiles are admitted to show possible modulation in its amplitude.