三个方程耦合的Schrödinger方程组的基态

研究由三个方程耦合的非线性Schr?dinger方程组,它们源于非线性光学和Bose-Einstein凝聚.考虑了两种类型:含有周期位势的方程组和含有势阱位势的方程组.借助于广义的Nehari流形以及精细的能量估计,证明了当相互作用位势适当小时,这两类非线性Schr?dinger方程组存在正的基态.     

三个方程耦合的Schr?dinger方程组的基态（英文）

研究由三个方程耦合的非线性Schr?dinger方程组,它们源于非线性光学和Bose-Einstein凝聚.考虑了两种类型:含有周期位势的方程组和含有势阱位势的方程组.借助于广义的Nehari流形以及精细的能量估计,证明了当相互作用位势适当小时,这两类非线性Schr?dinger方程组存在正的基态.     

非线性高阶抛物双曲型耦合方程组的第一边界问题

本文研究了一类广义Sine-Gordon型非线性高阶双曲方程组、非线性高阶拟双曲型方程组、非线性高阶拟抛物型方程组以及非线性高阶广义Sehrdinger型方程组的耦合方程组的第一边界问题,作者证明了此耦合方程组第一边界问题的整体广义解和整体古典解的存在性、唯一性和光滑性。     

高阶非线性双曲型拋物型耦合方程组的周期边界问题和初值问题

本文研究了广义Sine—Gordon型非线性高阶双曲方程组、高阶非线性拟双曲型方程组、高阶非线性拟抛物型方程组以及高阶非线性Schrodinger型方程组的耦合方程组的周期边界问题和初值问题。证明了此耦合方程组的周期边界问题和初值问题整体广义解和整体古典解的存在性、唯一性和光滑性。     

一类含临界耦合非线性项的奇异椭圆方程组的正解

本文研究了一类含临界指数与耦合非线性项的奇异椭圆方程组. 利用变分方法与极大值原理, 通过证明对应的能量泛函满足局部的 (PS)c 条件, 得到了这类方程组正解的存在性, 推广了单个方程与方程组中的相应结果.     

一些非线性发展方程的显式行波解

该文给出了一种构造非线性发展方程显式行波解的方法并用该方法得到了Hirota-Satsuma方程组,一类非线性常微分方程以及广义耦合标量场方程组的显式行波解.     

微重力环境下充液球腔非线性耦合动力学研究

采用球坐标系描述球腔中的液体动力学特性并建立一种轴对称贮腔类液刚耦合系统动力学模型.采用模态展开方法分析了微重环境下球形贮箱中的液体晃动问题,给出了球形贮箱内液体晃动速度势函数和波高函数的Gauss超几何级数解析表达式.采用变分原理推导了系统动力学系模型,利用Galerkin方法对变分方程进行特征频率分析.运用Lagrange方法及非线性动力学方法导出了微重力环境下贮箱中液体与航天器结构耦合的动力学方程组,并对该方程组进行了数值计算,绘出了非线性耦合充液系统自由度随时间的变化历程.     

含临界指数与Hardy项耦合椭圆系统的非平凡解

研究了一类含临界指数耦合非线性项的奇异椭圆方程组,通过对临界耦合非线性项的分析与精确的能量估计,利用环绕定理,得到了这类方程组非平凡解的存在性.     

耦合Schrdinger-KdV方程组Cauchy问题的适定性

本文研究了耦合Schrodinger－KdV方程组的Cauchy问题，此耦合方程组刻化了一维Langmuir和离子声波相互作用的非线性动力学行为．本文建立了此问题在Hk×Hk中的整体适定性理论（k∈Z+）．     

非线性耦合KdV方程组的一种新求解法

本文研究了构造非线性耦合Kd V方程组的无穷序列复合型新解的问题.利用函数变换与辅助方程相结合的方法,获得了非线性耦合Kd V方程组的自由Riemannθ函数、Jacobi椭圆函数、双曲函数和三角函数两两组合的无穷序列复合型新解.这些解包括了双弧子解、双周期解和弧子解与周期解复合的解.     

Free vibration analysis of a rigidly fixed viscothermoelastic hollow sphere

In this paper an exact analysis of homogenous rigidly fixed vibrations of viscothermoelastic hollow sphere is presented. The basic governing partial differential equations have been reduced to ordinary differential equations by using Helmholtz decomposition equations. The uncoupled equation is taken for first class vibrations and remains independent of temperature variations, while coupled system of equations are taken for second class vibrations. Matrix Fröbenious method of extended power series has been applied in the coupled system of differential equations to get displacements and temperature. Numerical results have been presented, giving lowest frequency, dissipation factor, displacements and temperature change.     

Symmetry group analysis and similarity solutions for the (2+1)‐dimensional coupled Burger's system

Symmetry group analysis and similarity reduction of nonlinear system of coupled Burger equations in the form of nonlinear partial differential equation are analyzed via symmetry method. The symmetry method has led to similarity reductions of this equation to solvable form to third‐order partial differential equation. The infinitesimal, similarity variables, dependent variables, and reduction have been tabulated. The search for solutions of these systems by using the improved tanh method has yielded certain exact solutions expressed by rational functions. Some figures are given to show the properties of the solutions. Copyright © 2013 John Wiley & Sons, Ltd.     

Asymptotic and spectral properties of operator‐valued functions generated by aircraft wing model

The present paper is devoted to the asymptotic and spectral analysis of an aircraft wing model in a subsonic air flow. The model is governed by a system of two coupled integro‐differential equations and a two parameter family of boundary conditions modelling the action of the self‐straining actuators. The differential parts of the above equations form a coupled linear hyperbolic system; the integral parts are of the convolution type. The system of equations of motion is equivalent to a single operator evolution–convolution equation in the energy space. The Laplace transform of the solution of this equation can be represented in terms of the so‐called generalized resolvent operator, which is an operator‐valued function of the spectral parameter. More precisely, the generalized resolvent is a finite‐meromorphic function on the complex plane having a branch‐cut along the negative real semi‐axis. Its poles are precisely the aeroelastic modes and the residues at these poles are the projectors on the generalized eigenspaces. The dynamics generator of the differential part of the system has been systematically studied in a series of works by the second author. This generator is a non‐selfadjoint operator in the energy space with a purely discrete spectrum. In the aforementioned series of papers, it has been shown that the set of aeroelastic modes is asymptotically close to the spectrum of the dynamics generator, that this spectrum consists of two branches, and a precise spectral asymptotics with respect to the eigenvalue number has been derived. The asymptotical approximations for the mode shapes have also been obtained. It has also been proven that the set of the generalized eigenvectors of the dynamics generator forms a Riesz basis in the energy space. In the present paper, we consider the entire integro‐differential system which governs the model. Namely, we investigate the properties of the integral convolution‐type part of the original system. We show, in particular, that the set of poles of the adjoint generalized resolvent is asymptotically close to the discrete spectrum of the operator that is adjoint to the dynamics generator corresponding to the differential part. The results of this paper will be important for the reconstruction of the solution of the original initial boundary‐value problem from its Laplace transform and for the analysis of the flutter phenomenon in the forthcoming work. Copyright © 2004 John Wiley & Sons, Ltd.     

Coupling three-field formulation and meshless mixed Galerkin methods using radial basis functions

In this work, we solve the elliptic partial differential equation by coupling the meshless mixed Galerkin approximation using radial basis function with the three-field domain decomposition method. The formulation has been adopted to increase the efficiency of the numerical technique by decreasing the error and dealing with the ill conditioning of the linear system caused by the radial basis function. Convergence analysis of the coupled technique is treated and numerical results of some solved examples are given at the end of this paper.     

On the rational solitary wave solutions for the nonlinear Hirota–Satsuma coupled KdV system

The objective of this article is to investigate an algebraic method for constructing new rational exact wave soliton solutions in terms of hyperbolic and triangular functions for the generalized nonlinear Hirota–Satsuma coupled KdV systems of partial differential equations using symbolic software like Mathematica or Maple. These studies reveal that the generalized nonlinear Hirota–Satsuma coupled KdV system has a rich variety of solutions.     

一类爆炸凝结过程的数学模型

所建立的数学模型是由可数无穷多个彼此相互关联的非线性常微分方程所组成的自治系统,它刻划了在只有基本粒子与i-粒子(i≥1)进行碰撞反应的系统里,粒子增长过程中密度随时间的变化规律.本文研究了这一自治系统解的性质.     

An existence result for elliptic partial differential-algebraic equations arising in semiconductor modeling

We consider a system of partial differential-algebraic equations which model an electric network containing semiconductor devices. The zero-dimensional differential-algebraic network equations are coupled with multi-dimensional elliptic partial differential equations which model the devices. For this coupled system we prove an existence result.     

Heat and mass transfer in MHD non-Darcian flow of a micropolar fluid over a stretching sheet embedded in a porous media with non-uniform heat source and thermal radiation

A mathematical analysis has been carried out to study magnetohydrodynamic boundary layer flow, heat and mass transfer characteristic on steady two-dimensional flow of a micropolar fluid over a stretching sheet embedded in a non-Darcian porous medium with uniform magnetic field. Momentum boundary layer equation takes into account of transverse magnetic field whereas energy equation takes into account of Ohmic dissipation due to transverse magnetic field, thermal radiation and non-uniform source effects. An analysis has been performed for heating process namely the prescribed wall heat flux (PHF case). The governing system of partial differential equations is first transformed into a system of non-linear ordinary differential equations using similarity transformation. The transformed equations are non-linear coupled differential equations which are then linearized by quasi-linearization method and solved very efficiently by finite-difference method. Favorable comparisons with previously published work on various special cases of the problem are obtained. The effects of various physical parameters on velocity, temperature, concentration distributions are presented graphically and in tabular form.     

Analytical particular solutions of augmented polyharmonic spline associated with Mindlin plate model

Analytical particular solutions of the augmented polyharmonic spline (APS) associated with the polyharmonic and poly‐Helmholtz operators and their products were derived by Tsai et al. (Eng Anal Bound Elem 33 (2009), 514). In addition, it has been mentioned that the particular solution associated with a coupled system of partial differential equations (PDEs) can be derived from the prescribed solutions by using the Hörmander operator decomposition technique. In this article, this derivation procedure is demonstrated via Mindlin thick‐plate problems, which are governed by a coupled system of three second‐order PDEs. Analytical particular solutions of displacements, shear forces, and bending or twisting moments corresponding to the polyharmonic spline and monomials are all explicitly derived. These particular solutions are validated using numerical examples. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

Qualitative analysis of a coupled reaction-diffusion model in biology with time delays

Certain biochemical reaction can be modeled by a coupled system of time-delayed ordinary differential equations and linear parabolic partial differential equations. In a three-compartment model these equations are coupled through the boundary conditions. The aim of this paper is to give a qualitive analysis of this unusual coupled system. The analysis includes the existence and uniqueness of a global solution, explicit upper and lower bounds of the solution, and global stability of a steady-state solution. The global stability result is with respect to any nonnegative initial perturbation and is independent of the time delays in the process of reaction. Special attention is given to the Goodwin model for biochemical control of genes by a negative feedback mechanism with time delay and diffusion.