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Moving Matter-Wave Solitons in Spin-Orbit Coupled Bose-Einstein Condensates

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Chinese Physics Letters 2016年第10期33卷 24-27页

作者：李玉娥薛具奎 Key Laboratory of Atomic and Molecular Physics and Functional Materials of Gansu Province College of Physics and Electronics EngineeringNorthwest Normal University

We investigate the moving matter-wave solitons in spin-orbit coupled Bose Einstein condensates （BECs） by a perturbation method. Starting with the one-dimensional Gross Pitaevskii equations, we derive a new KdV-like equation to which an approximate solution is obtained by assuming weak Raman coupling and strong spin orbit coupling. The derivation of the KdV-like equation may be useful to understand the properties of solitons excitation in spin-orbit coupled BECs. We find different types of moving solitons： dark-bright, bright bright and dark dark solitons. Interestingly, moving dark-dark soliton for attractive intra- and inter-species interactions is found, which depends on the Raman coupling. The amplitude and velocity of the moving solitons strongly depend on the Raman coupling and spin orbit coupling.

关键词： of on in Moving Matter-Wave Solitons in Spin-Orbit Coupled Bose-Einstein Condensates KdV for like line is

Painleve Integrability, Consistent Riccati Expansion Solvability and Interaction Solution for the Coupled mKdV-BLMP System

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Chinese Physics Letters 2017年第1期34卷 1-5页

作者：陈俊超马正义胡亚红 Department of Mathematics Lishui University

The integrability of the coupled, modified KdV equation and the potential Boiti-Leon-Manna-Pempinelli (mKdV-BLMP) system is investigated using the Painlevé analysis approach. It is shown that this coupled system possesses the Painlevé property in both the principal and secondary branches. Then, the consistent Riccati expansion (CRE) method is applied to the coupled mKdV-BLMP system. As a result, it is CRE solvable for the principal branch while non-CRE solvable for the secondary branch. Finally, starting from the last consistent differential equation in the CRE solvable case, soliton, multiple resonant soliton solutions and soliton-cnoidal wave interaction solutions are constructed explicitly.

关键词： KdV Painleve Integrability Consistent Riccati Expansion Solvability and Interaction Solution for the Coupled mKdV-BLMP System

A Jacobi Spectral Collocation Scheme Based on Operational Matrix for Time-fractional Modified Korteweg-de Vries Equations

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Computer Modeling in Engineering & Sciences 2015年第3期104卷 185-209页

作者： A.H.Bhrawy E.H.Doha S.S.Ezz-Eldien M.A.Abdelkawy Department of Mathematics Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia Department of Mathematics Faculty of ScienceBeni-Suef UniversityBeni-SuefEgypt Department of Mathematics Faculty of ScienceCairo UniversityGizaEgypt Department of Mathematics Faculty of ScienceAssiut UniversityNew Valley BranchEl-Kharja 72511Egypt

In this paper,a high accurate numerical approach is investigated for solving the time-fractional linear and nonlinear Korteweg-de Vries(KdV)equations.These equations are the most appropriate and desirable definition for physical modeling.The spectral collocation method and the operational matrix of fractional derivatives are used together with the help of the Gauss-quadrature formula in order to reduce such problem into a problem consists of solving a system of algebraic equations which greatly simplifying the problem.Our approach is based on the shifted Jacobi polynomials and the fractional derivative is described in the sense of Caputo.In addition,the presented approach is applied also to solve the timefractional modified KdV equation.For testing the accuracy,validity and applicability of the developed numerical approach,we apply it to provide high accurate approximate solutions for four test problems.

关键词： KdV equation Jacobi polynomials Operational matrix Gauss quadrature Collocation spectral method Caputo derivative

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Communications in Theoretical Physics 2013年第3期59卷 263-267页

作者：智红燕 College of Science China University of Petroleum

In this paper,some new formal similarity reduction solutions for the(2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived.Firstly,we derive the similarity reduction of the NNV equation with the optimal system of the admitted one-dimensional subalgebras.Secondly,by analyzing the reduced equation,three types of similarity solutions are derived,such as multi-soliton like solutions,variable separations solutions,and KdV type solutions.

关键词：相似约化代数方程分析公式变量分离相似性 KdV 类型一维

Relationship Between the Restricted AKNS Flows and the Restricted KdV Flows

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Chinese Annals of Mathematics,Series B 2012年第2期33卷 191-206页

作者： Ruguang ZHOU School of Mathematical Sciences Xuzhou Normal UniversityXuzhou 221116JiangsuChina.

It is well-known that every member of the KdV hierarchy of equations can be obtained from the AKNS hierarchy of equations by imposing a simple reduction.The author finds that the reduction conditions of the potentials in the spectral problem can be replaced by adding additional eigenfunction equations to the spectral problem,and then shows that the restricted KdV flows,such as the Neumann system,the Garnier system and the generalized multicomponent H'enon-Hieles system,are a kind of special reductions of the restricted AKNS flows.

关键词： KdV 流动诺伊曼系统函数方程 AKNS族谱问题

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Communications in Theoretical Physics 2010年第3期53卷 575-578页

作者： K. Fakhar T. Hayat CHENG Yi N. Amin Department of Mathematics Faculty of Science Universiti Teknologi Malaysia 81310 UTM Skudai Johor Malaysia Department of Mathematics Universily of Science and Technology of China Hefei Anhui 230026 China

This note looks at the two similarity solutions of the Navier-Stokes equations in polar coordinates. In the second solution an initial value problem is reduced into generalized stationary KdV and hence integrable.

关键词： Stokes方程相似解作者注记斯托克斯方程初始值问题 KdV

Conditional Lie-Bcklund Symmetry and New Variable Separation Solutions of the Third Order KdV-Type Equations

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Communications in Theoretical Physics 2018年第10期70卷 399-404页

作者：屈改珠张顺利李海侠王岗伟 School of Mathematics and Physics Weinan Normal University Center for Nonlinear Studies School of Mathematics Northwest University Institute of Mathematics Science Baoji University of Arts and Sciences School of Mathematics and Statistics Hebei University of Economics and Business

The functionally generalized variable separation solutions of a general KdV-type equations u_t=u_(xxx) +A(u, u_x)u_(xx) + B(u, u_x) are investigated by developing the conditional Lie-Backlund symmetry method. A complete classification of the considered equations, which admit multi-dimensional invariant subspaces governed by higher-order conditional Lie-B¨acklund symmetries, is presented. As a result, several concrete examples are provided to construct functionally generalized variable separation solutions of some resulting equations.

关键词：对称方法分离解 KdV 方程可变类型机能多维

Constraints and Soliton Solutions for KdV Hierarchy and AKNS Hierarchy

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理论物理通讯：英文版 2011年第10期56卷 605-610页

作者：李年华李玉奇 Center for Nonlinear Science Ningbo University

It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator. We generalize the result to a special form of Lax pair,from which a method to constrain the integrable system to a lower-dimensional or fewer variable integrable system is proposed.A direct result is that the n-soliton solutions of the KdV hierarchy can be completely depicted by a series of ordinary differential equations(ODEs),which may be gotten by a simple but unfamiliar Lax pair.Furthermore the AKNS hierarchy is constrained to a series of univariate integrable hierarchies.The key is a special form of Lax pair for the AKNS hierarchy.It is proved that under the constraints all equations of the AKNS hierarchy are linearizable.

关键词：孤子解 KdV KdV方程常微分方程 Lax对可积系统层次结构运算符

KAM Theory for Partial Differential Equations

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Analysis in Theory and Applications 2019年第3期35卷 235-267页

作者： Massimiliano Berti Massimiliano Berti SISSA

In the last years much progress has been achieved in KAM theory concerning bifurcation of quasi-periodic solutions of Hamiltonian or reversible partial differential equations.We provide an overview of the state of the... 详细信息

关键词： KAM for PDEs quasi-periodic solutions small divisors infinite dimensional Hamiltonian and reversible systems water waves nonlinear wave and Schr?dinger equations KdV