Multi-soliton solutions, breather-like and bound-state solitons for complex modified Korteweg–de Vries equation in optical fibers

Under investigation in this paper is a complex modified Korteweg–de Vries(KdV) equation, which describes the propagation of short pulses in optical fibers. Bilinear forms and multi-soliton solutions are obtained through the Hirota method and symbolic computation. Breather-like and bound-state solitons are constructed in which the signs of the imaginary parts of the complex wave numbers and the initial separations of the two parallel solitons are important factors for the interaction patterns. The periodic structures and position-induced phase shift of some solutions are introduced.

Multi-soliton solutions for the coupled modified nonlinear Schrdinger equations via Riemann–Hilbert approach

The coupled modified nonlinear Schrodinger equations are under investigation in this work. Starting from analyzing the spectral problem of the Lax pair, a Riemann-Hilbert problem for the coupled modified nonlinear Schrodinger equations is formulated. And then, through solving the obtained Riemann-Hilbert problem under the conditions of irregularity and reflectionless case, N-soliton solutions for the equations are presented. Furthermore, the localized structures and dynamic behaviors of the one-soliton solution are shown graphically.

Head-on collision between single-and multi-soliton heavy ion acoustic waves in multi-ion plasmas

Head-on collisions among the single-and multi-soliton’s heavy ion acoustic waves(HIAWs) of multi-ion plasma are studied. The plasma consists of adiabatic positively charged inertial heavy ions, Boltzmann energy distributed light ions and kappa energy distributed electrons. The extended poincaré-Lighthill-Kuo(e PLK) method is applied for the derivation of two-sided Korteweg–de Vries(KdV) equations(KdVEs). The KdV single-soliton solutions(KdVSSs) are determined using the hyperbolic secant method and the KdV multi-soliton solutions(KdVMSs)are obtained using the Hirota method. The effects of superthermality of electrons, temperature ratios of electron to light ion and heavy ion to electron, and the density ratio of electron to heavy ion on phase shifts are investigated for the head-on collisions between two-soliton HIAWs. The effects of plasma parameters on angular frequency, phase speed, production of multi-soliton structures, and the head-on collisions among single-, double-, triple-, quadruple-, and quintuplesolitons are also studied.

Cross-kink multi-soliton solutions for the (3+1)-D Jimbo-Miwa equation

In this paper, by using bilinear form and extended three-wave type of ans¨atz approach, we obtain new cross-kink multi-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equation, including the periodic breather-type of kink three-soliton solutions, the cross-kink four-soliton solutions, the doubly periodic breathertype of soliton solutions and the doubly periodic breather-type of cross-kink two-soliton solutions. It is shown that the generalized three-wave method, with the help of symbolic computation, provides an effective and powerful mathematical tool for solving high dimensional nonlinear evolution equations in mathematical physics.

简化的双线性法求Lax型7阶KdV方程的多孤子解

应用简化的双线性方法研究由Lax导出的7阶KdV方程.通过一些辅助函数的特殊表达式作为解的假设,利用数学软件计算获得了该方程的两孤子解和三孤子解,并给出两孤子解和三孤子解的三维图和二维图,直观地显示了这两种孤子解的动力学行为,同时也体现了简化的双线性方法在解可积方程中的有效性.

Chaotic behaviors of the (2+1)-dimensional generalized Breor-Kaup system

With the help of the Maple symbolic computation system and the projective equation approach,a new family of variable separation solutions with arbitrary functions for the（2＋1）-dimensional generalized Breor-Kaup（GBK） system is derived.Based on the derived solitary wave solution,some chaotic behaviors of the GBK system are investigated.

Ranking approach of cross-efficiency based on improved TOPSIS technique

The cross-efficiency evaluation method is reviewed which is developed as a data envelopment analysis （DEA） extensive tool. The cross-efficiency evaluation method is utilized to identify the decision making unit （DMU） with the best practice and to rank the DMUs by their respective cross-efficiency scores. The main drawbacks of the cross-efficiency evaluation method when the ultimate average cross-efficiency scores are used to evalu- ate and rank the DMUs are also pointed out. With the research gap, an improved technique for order preference by similarity to ideal solution （TOPSIS） is introduced to rank the crossfficiency by eliminating the average assumption. Finally, an empirical example is illustrated to examine the validity of the proposed method.

Orientation and Structure of Ionic Liquid Cation at Air/[bmim][BF4] Aqueous Solution Interface

The watermiscible room temperature ionic liquid 1butyl3methylimidazolium tetrafluorob orate （[bmim] [BF4]） is a model system for studying the interactions between ionic liquid and water molecules. In this work the orientational structure of the low concentrated aqueous solution of [bmim] [BF4] at the air/liquid interface was investigated by sum frequency gener ation vibrational spectroscopy. It has been found that at very low concentrations, the butyl chain exhibited a significant gauche defect, indicating a disordered conformation; and the cation ring oriented with a fairly small tilting angle at the surface. When the concentration increased, the cation ring tended to lie flat at the surface, and the gauche defects of the butyl chain decreased due to the intermolecular chainchain interactions and the consequent more ordered interfacial molecular arrangement. Additionally, the antisymmetric stretching mode in the PPP and SPS spectra exhibited a peak shift, showing that there exists more than one kind of orientation or chemical environment for the butyl CH3 group. These results may shed new light on understanding the surface behavior of watermiscible ionic liquids as well as the imidazolium based surfactants.

GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS FOR GENERALIZED POCHHAMMER-CHREE EQUATIONS

In this article, we study the initial boundary value problem of generalized Pochhammer-Chree equation utt-uxx-uxxt-uxxtt=f（u）xx,x∈Ω,t〉0,u（x,0）=u0（x）,ut（x,0）=u1（x）,x∈Ω,u（0,t）=u（1,t）=0,t≥0, where Ω = （0, 1）. First, we obtain the existence of local Wkp solutions. Then, we prove that, if f（s） ∈ Ck＋1（R） is nondecreasing, f（0） = 0 and ｜f（u）｜ ≤ C1｜u｜∫0uf（s）ds ＋ C2, u0（x）,u1（x） ∈ WkP（Ω） ∩ W01,P（Ω）, k≥ 1, 1 〈 p≤ ∞, then for any T 〉 0 the problem admits a unique solution u（x, t） ∈ W2,∞（0, T; WkP（Ω） ∩ W01,P（Ω））. Finally, the finite time blow-up of solutions and global Wkp solution of generalized IMBo equations are discussed.

Sufficient Optimality Conditions for Multiobjective Programming Involving (V, ρ)h,ψ-type Ⅰ Functions

New classes of functions namely (V, ρ)_(h,φ)-type I, quasi (V, ρ)_(h,φ)-type I and pseudo (V, ρ)_(h,φ)-type I functions are defined for multiobjective programming problem by using BenTal's generalized algebraic operation. The examples of (V, ρ)_(h,φ)-type I functions are given. The sufficient optimality conditions are obtained for multi-objective programming problem involving above new generalized convexity.

Darboux Transformation and New Soliton-like Solutions for （1＋1）-Dimensional Higher-Order Broer-Kaup System

In this letter, we construct a kind of new Darboux transformation for the （1＋1）-dimensional higher-order Broer-Kaup （HBK） system with the help of a gauge transformation of a spectral problem. By applying this new Darboux transformation, some new soliton-like solutions of the （1＋1）-dimensional HBK system are obtained.

Darboux Transformation and Solitons for Reduced Maxwell-Bloch Equations

The Darboux transformations from arbitrary solutions of reduced Maxwell-Bloch equations is constructed in this article. Hence, in principle, we can find multi-soliton solutions by algebric algorithm, and the formula will be given explicitly.

N-Fold Darboux Transformation and Bidirectional Solitons for Whitham-Broer-Kaup Model in Shallow Water

Under investigation in this paper is the Whitham-Broer-Kaup (WBK) system, which describes the dispersive long wave in shallow water. Through a variable transformation, the WBK system is casted into a general Broer-Kaup system whose Lax pair can be derived by the Ablowitz-Kaup-Newell-Segur technology. With symbolic computation, based on the aforementioned Lax pair, the N-fold Darboux transformation is constructed with a gauge transformation and the multi-soliton solutions are obtained. Finally, the elastic interactions of the two-soliton solutions (including the head-on and overtaking collisions) for the WBK system are graphically studied. Those multi-soliton collisions can beused to illustrate the bidirectional propagation of the waves in shallow water.

Solitons for the cubic-quintic nonlinear Schrdinger equation with varying coefficients

In this paper,by means of similarity transfomations,we obtain explicit solutions to the cubic-quintic nonlinear Schr顜僤inger equation with varying coefficients,which involve four free functions of space.Four types of free functions are chosen to exhibit the corresponding nonlinear wave propagations.

Benchmark solutions for sound propagation in an ideal wedge

Sound propagation in a wedge-shaped waveguide with perfectly reflecting boundaries is one of the few range- dependent problems with an analytical solution, and hence provides an ideal benchmark for a full two-way solution to the wave equation. An analytical solution for the sound propagation in an ideal wedge with a pressure-release bottom was presented by Buckingham and Tolstoy [Buckingham and Tolstoy 1990 J. Acoust. Soc. Am. 87 1511]. The ideal wedge problem with a rigid bottom is also of great importance in underwater acoustics. We present an analytical solution to the ideal wedge problem with a perfectly reflecting bottom, either rigid or pressure-release, which may be used to provide a means for investigating the sound field in depth-varying channels, and to establish the accuracy of numerical propagation models. Closed-form expressions for coupling matrices are also provided for the ideal waveguides characterized by a ho- mogeneous water column bounded by perfectly reflecting boundaries. A comparison between the analytical solution and the numerical solution recently proposed by Luo et al. [Luo W Y, Yang C M and Zhang R H 2012 Chin. Phys. Lett. 29 014302] is also presented, through which the accuracy of this numerical model is illustrated.

Variational iteration method for solving compressible Euler equations

This paper applies the variational iteration method to obtain approximate analytic solutions of compressible Euler equations in gas dynamics. This method is based on the use of Lagrange multiplier for identification of optimal values of parameters in a functional. Using this method, a rapid convergent sequence is produced which converges to the exact solutions of the problem. Numerical results and comparison with other two numerical solutions verify that this method is very convenient and efficient.

The dynamics of nonstationary solutions in one-dimensional two-component Bose-Einstein condensates

This paper investigates the dynamical properties of nonstationary solutions in one-dimensional two-component Bose-Einstein condensates. It gives three kinds of stationary solutions to this model and develops a general method of constructing nonstationary solutions. It obtains the unique features about general evolution and soliton evolution of nonstationary solutions in this model.

CONVERGENCE FROM THE TWO-SPECIES VLASOV-POISSON-BOLTZMANN SYSTEM TO THE TWO-FLUID INCOMPRESSIBLE NAVIER-STOKES-FOURIER-POISSON SYSTEM WITH OHM'S LAW

In this paper,we justify the convergence from the two-species Vlasov-PoissonBoltzmann(VPB,for short)system to the two-fluid incompressible Navier-Stokes-FourierPoisson(NSFP,for short)system with Ohm’s law in the context of classical solutions.We prove the uniform estimates with respect to the Knudsen numberεfor the solutions to the two-species VPB system near equilibrium by treating the strong interspecies interactions.Consequently,we prove the convergence to the two-fluid incompressible NSFP asεgoes to 0.

Nonautonomous bright solitons and soliton collisions in a nonlinear medium with an external potential

We present exact bright multi-soliton solutions of a generalized nonautonomous nonlinear Schroinger equation with time-and space-dependent distributed coefficients and an external potential which describes a pulse propagating in nonlinear media when its transverse and longitudinal directions are nonuniformly distributed.Such solutions exist in certain constraint conditions on the coefficients depicting dispersion,nonlinearity,and gain（loss）.Various shapes of bright solitons and interesting interactions between two solitons are observed.Physical applications of interest to the field and stability of the solitons are discussed.

Diverse soliton solutions and dynamical analysis of the discrete coupled mKdV equation with 4×4 Lax pair

Under consideration in this study is the discrete coupled modified Korteweg-de Vries(mKdV)equation with 4×4 Lax pair.Firstly,through using continuous limit technique,this discrete equation can be mapped to the coupled KdV and mKdV equations,which may depict the development of shallow water waves,the optical soliton propagation in cubic nonlinear media and the Alfven wave in a cold collision-free plasma.Secondly,the discrete generalized(r,N-r)-fold Darboux transformation is constructed and extended to solve this discrete coupled equation with the fourth-order linear spectral problem,from which diverse exact solutions including usual multi-soliton and semi-rational soliton solutions on the vanishing background,higher-order rational soliton and mixed hyperbolic-rational soliton solutions on the non-vanishing background are derived,and the limit states of some soliton and rational soliton solutions are analyzed by the asymptotic analysis technique.Finally,the numerical simulations are used to explore the dynamical behaviors of some exact soliton solutions.These results may be helpful for understanding some physical phenomena in fields of shallow water wave,optics,and plasma physics.