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Abstract: The bilinear form of a coupled modified KdV equations with non-uniformity terms is given and a few soliton solutions are obtained. Furthermore, the multisoliton of the coupled system is expressed by Pfaffian. [Copyright &y& Elsevier]

Abstract: In this Letter, a variable-coefficient discrete tanh method is proposed for solving nonlinear differential–difference equations. With the aid of symbolic computation, we choose a ()-dimensional Toda equation to illustrate the validity and advantages of the method. As a result, hyperbolic function solutions, trigonometric function solutions and rational solutions with arbitrary functions are obtained. It is shown that the proposed method provides a powerful mathematical tool for nonlinear differential–difference equations in mathematical physics. [Copyright &y& Elsevier]

Abstract: In this Letter, the Exp-function method is generalized to construct N-soliton solutions of a KdV equation with variable coefficients. As a result, 1-soliton, 2-soliton and 3-soliton solutions are obtained, from which the uniform formula of N-soliton solutions is derived. It is shown that the Exp-function method may provide us with a straightforward and effective mathematical tool for generating N-soliton solutions of nonlinear evolution equations in mathematical physics. [Copyright &y& Elsevier]

Abstract: In this Letter, with the help of Hermit transformation, we employ the Riccati equation and its new exact solutions to find new exact solutions of -dimensional stochastic Broer–Kaup equation in the white noise environment. As some special examples, some analytic solutions can degenerate into these solutions reported in open literatures. [Copyright &y& Elsevier]

Abstract: In this Letter, an algorithm is devised for using the -expansion method to solve nonlinear differential-difference equations. With the aid of symbolic computation, we choose two discrete nonlinear lattice equations to illustrate the validity and advantages of the algorithm. As a result, hyperbolic function solutions and trigonometric function solutions with parameters are obtained. When the parameters are taken as special values, some known solutions including kink-type solitary wave solution and singular travelling wave solution are recovered. It is shown that the proposed algorithm is effective and can be used for many other nonlinear differential-difference equations in mathematical physics. [Copyright &y& Elsevier]

Abstract: A mathematical technique based on an auxiliary equation and the symbolic computation system Matlab is developed to construct the exact solutions for a generalized Camassa–Holm equation and a nonlinear dispersive equation with variable coefficients. It is shown that the variable coefficients of the derivative terms in the equations cause the qualitative change in the physical structures of the solutions. [Copyright &y& Elsevier]

Abstract: In this Letter, Exp-function method is employed to obtain traveling wave solutions of the Fisher equation. It is shown that, on this example, the Exp-function method is easy to implement and concise method for nonlinear evolution equations in mathematical physics. [Copyright &y& Elsevier]

Abstract: The quantum hydrodynamic model is employed to study the nonlinear structure of non-planar dust acoustic waves in quantum dusty plasmas consisting of electrons, ions, and negatively/positively charged dust particles. A Kadomstev–Petviashvili equation is derived in cylindrical geometry. Based on the analytical solution, it is found that the Nebulon structure is significantly modified by the quantum effects including quantum diffraction effect and quantum statistical effect. [Copyright &y& Elsevier]

Abstract: In this Letter, a generalized -expansion method is proposed to seek exact solutions of nonlinear evolution equations. Being concise and straightforward, this method is applied to the mKdV equation with variable coefficients. As a result, hyperbolic function solution, trigonometric function solution and rational solution with parameters are obtained. When the parameters are taken as special values, two known kink-type solitary wave solutions are derived from the hyperbolic function solution. It is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations in mathematical physics. [Copyright &y& Elsevier]

Abstract: In this Letter, the Exp-function method is used to seek generalized solitonary solutions of Riccati equation. Based on the Riccati equation and its generalized solitonary solutions, new exact solutions with three arbitrary functions of the ()-dimensional Broer–Kaup–Kupershmidt equations are obtained. It is shown that the Exp-function method provides a straightforward and important mathematical tool for nonlinear evolution equations in mathematical physics. [Copyright &y& Elsevier]

Abstract: We examine collisions of moving solitons in a fiber Bragg grating with a triplet composed of two closely set repulsive defects of the grating and an attractive one inserted between them. A doublet (dipole), consisting of attractive and repulsive defects with a small distance between them, is considered too. Systematic simulations demonstrate that the triplet provides for superior results, as concerns the capture of a free pulse and creation of a standing optical soliton, in comparison with recently studied traps formed by single and paired defects, as well as the doublet: 2/3 of the energy of the incident soliton can be captured when its velocity attains half the light speed in the fiber (the case most relevant to the experiment), and the captured soliton quickly relaxes to a stationary state. A subsequent collision between another free soliton and the pinned one is examined too, demonstrating that the impinging soliton always bounces back, while the pinned one either remains in the same state, or is kicked out forward, depending on the collision velocity and phase shift between the solitons. [Copyright &y& Elsevier]

Abstract: We study linear excitations to a one-dimensional dark soliton described by a defocusing nonlinear Schödinger equation. By solving an eigenvalue problem for the excitations we obtain all eigenvalues and eigenfunctions and prove rigorously that these eigenfunctions are orthonormal and form a complete set. We then use the eigenfunctions to obtain the exact form of linear excitations for any given initial condition and to investigate the transverse stability of the dark soliton. The rigorous results reported in the present work can be applied to study the dynamics of dark solitons in various nonlinear optical media and Bose–Einstein condensates. [Copyright &y& Elsevier]

Abstract: In this Letter, the Exp-function method is used to seek exact solutions of Maccari''s system. As a result, single and combined generalized solitonary solutions are obtained, from which some known solutions obtained by extended sine-Gordon equation method and improved hyperbolic function method are recovered as special cases. It is shown that the Exp-function method provides a very effective and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. [Copyright &y& Elsevier]

Abstract: Properties of localized states on array of BEC confined to a potential, representing superposition of linear and nonlinear optical lattices are investigated. For a shallow lattice case the coupled mode system has been derived. We revealed new types of gap solitons and studied their stability. For the first time a moving soliton solution has been found. Analytical predictions are confirmed by numerical simulations of the Gross–Pitaevskii equation with jointly acting linear and nonlinear periodic potentials. [Copyright &y& Elsevier]

Abstract: The tanh–coth method and the sech method are used to construct many exact solutions for Jaulent–Miodek equation. Travelling wave solutions are determined. Complex solutions are obtained as well. The power of the proposed methods is confirmed. [Copyright &y& Elsevier]

Abstract: A generalized method with computerized symbolic computation, which is called the generalized extended tanh-function method, is presented for the nonlinear equations of mathematical physics (NEMPs). Compared with most of the existing tanh-function method, the extended tanh-function method, the modified extended tanh-function method and generalized hyperbolic-function method, the proposed method is more powerful. By use of the method, we not only can successfully recover the previously known formal solutions but also construct new and more general formal solutions for some NEMPs. Make use of the method, we study the -dimensional potential-YTSF equation and obtain rich new families of the exact solutions, including the nontraveling wave and coefficient functions'' soliton-like solutions, singular soliton-like solutions. [Copyright &y& Elsevier]

Abstract: We investigate stability of localized time-periodic states (pulsons) of a real scalar field satisfying the Klein–Gordon equation with the logarithmic nonlinearity. It is shown that the pulsons of any amplitudes, remaining well-localized objects, lose their coherence with time. We thus conclude that, strictly speaking, all pulsons of the model considered are unstable. Nevertheless, for some amplitudes the rate of the coherence breaking is found to be very small, so that the corresponding pulsons are long-lived. [Copyright &y& Elsevier]