具调和振子的非线性Schrodinger方程

考虑具调和振子的非线性Schrodinger方程的Cauchy问题，采用Galerkin方法证明了整体强解的存在性，使用能量估计方法证明了整体强解的唯一性。     

一类具积分项非线性梁方程整体解的存在性

讨论了一类在轴向载荷作用下,有限长粘弹性梁的非线性振动问题,用Galerkin方法证明了问题的整体强解和整体经典解的存在性.     

一类多维非线性复抛物型方程组的整体解

本文考虑一类多维非线性复抛物型方程组的初边值问题和柯西问题,采用Galerkin方法和紧性原理,证明了这些问题整体强解与整体古典解的存在性、唯一性和正则性。     

一类四阶非线性波动方程的初边值问题

本文研究一类描述非线性粘弹性杆中纵波振动的非线性波动方程的初边值问题,用Ｇａｌｅｒｋｉｎ方法证明了其整体强解的存在性,唯一性,最后讨论了解的渐近性质及在一定条件下整体解的不存在性。     

一类非线性卷积拟抛物型积分微分方程整体解的存在性问题

本文研究一类非线性卷积拟抛物型积分微分方程的初边值问题,是运用Galerkin方法结合能量型先验估计证明了其整体强解的存在性、唯一性和正则性，并在一定条件下讨论了整体解的不存在性．     

方程Utt—△Ut=f（u）的整体解

本文用Galerkin方法研究多维非线性拟双曲方程u_(tt)-Δu_t=f(u)的初边值问题与初值问题的整体广义解的存在性及整体强解的存在和唯一性,得到了与对应的非线性波动方程截然不同的很有意义的结果。这一结果从一个方面充分体现了非线性拟双曲方程与非线性双曲方程根本不同的特征。     

非线性拟抛物型积分微分方程的初边值问题和初值问题

本文研究非线性拟抛物积分微分方程的初边值问题和初值问题。运用Galerkin方程结合能量估计证明了问题的整体强解的生存性、唯一性和稳定性，最后在一定条件下讨论了初边值问题整体解的不存在性和爆破问题。     

一类非线性发展方程整体强解的渐近行为

本文研究一类非线性高阶发展方程ua-△ui，-0△ua-△i=f（u）整体强解的渐近行为，利用ω极限紧方法得到了整体强解的全局吸引子 的存在性， 在D（A）×D（A）不变、紧，并且按D（A）×D（A）的范数吸引D（A）×D（A）中的任意有界集，其中非线性项f满足临界指数增长条件．     

一类流固耦合系统强解的存在性问题

本文主要讨论一类多刚体与粘性系数依赖于密度的不可压缩流体耦合系统的强解存在性问题.首先,利用变量替换建立本文研究对象对应的非线性微分方程,然后,利用Garlerkin逼近方法获得线性化问题的光滑解,从而可以构造出原问题的逼近解.通过估计逼近解的一致有界性,最后证明了一类描述多刚体在不可压缩流体中运动的耦合系统强解的存在...     

一类半线性双温度热传导方程整体强解的存在性

给出了一类半线性双温度热传导方程的初边值问题整体强解的存在条件,利用位势井方法证明了整体强解的存在性定理,且证明了方程的解或解对X的某些导数的L^2模估计式．     

Covariance and the hierarchy of frame bundles

This is an essay on the general concept of covariance, and its connection with the structure of the nested set of higher frame bundles over a differentiable manifold. Examples of covariant geometric objects include not only linear tensor fields, densities and forms, but affinity fields, sectors and sector forms, higher order frame fields, etc., often having nonlinear transformation rules and Lie derivatives. The intrinsic, or invariant, sets of forms that arise on frame bundles satisfy the graded Cartan-Maurer structure equations of an infinite lie algebra. Reduction of these gives invariant structure equations for Lie pseudogroups, and forG-structures of various orders. Some new results are introduced for prolongation of structure equations, and for treatment of Riemannian geometry with higher-order moving frames. The use of invariant form equations for nonlinear field physics is implicitly advocated.Research sponsored by the U.S. Army Research Office through an agreement with the National Aeronautics and Space Administration.     

The Drazin inverse in multibody system dynamics

Summary The numerical analysis of multibody system dynamics is based on the equations of motion as differential-algebraic systems. A thorough analysis of the linearized equations and their solution theory leads to an equivalent system of ordinary differential equations which gives deeper insight into the derivation of integration schemes and into the stabilization approaches. The main tool is the Drazin inverse, a generalized matrix inverse, which preserves the eigenvalues. The results are illustrated by a realistic truck model. Finally, the approach is extended to the nonlinear index 2 formulation.     

Symbolic software for soliton theory

Four symbolic programs, in Macsyma or Mathematica language, are presented. The first program tests forthe existence of solitons for nonlinear PDEs. It explicitly constructs solitons using Hirota's bilinear method. In the second program, the Painlevé integrability test for ODEs and PDEs is implemented. The third program provides an algorithm to compute conserved densities for nonlinear evolution equations. The fourth software package aids in the computation of Lie symmetries of systems of differential and difference-differential equations. Several examples illustrate the capabilities of the software.Research supported in part by NSF under Grant CCR-9300978.     

非线性森林发展系统的渐近性

本讨论他一类非线性森林发展系统,利用临界增生率要概念和算子的实特征值,讨论了系统解的渐近性质。     

Explicit traveling wave solutions of five kinds of nonlinear evolution equations

First of all, by using Bernoulli equations, we develop some technical lemmas. Then, we establish the explicit traveling wave solutions of five kinds of nonlinear evolution equations: nonlinear convection diffusion equations (including Burgers equations), nonlinear dispersive wave equations (including Korteweg-de Vries equations), nonlinear dissipative dispersive wave equations (including Ginzburg-Landau equation, Korteweg-de Vries-Burgers equation and Benjamin-Bona-Mahony-Burgers equation), nonlinear hyperbolic equations (including Sine-Gordon equation) and nonlinear reaction diffusion equations (including Belousov-Zhabotinskii system of reaction diffusion equations).     

Error estimates for MAC-like approximations to the linear Navier-Stokes equations

Summary In this paper a priori error estimates are derived for the discretization error which results when the linear Navier-Stokes equations are solved by a method which closely resembles the MAC-method of Harlow and Welch. General boundary conditions are permitted and the estimates are in terms of the discreteL ² norm. A solvability result is given which also applies to a generalization of the method to the nonlinear case. This generalization is used in the last section to produce a numerical solution to the problem of flow around an obstacle.This work supported in part by Westinghouse Nuclear Energy Systems. Research Report #76-13     

一类模糊非线性方程组及解法

模糊非线性方程组 ,在模糊控制和现实生活中很普遍 .本文考虑一类模糊非线性方程组的性质 ,然后给出一种解法 .首先把模糊非线性方程组转变成非线性规划 ,再用非线性规划中的方法或软件来解 .     

Admissible equivalence transformations for linearization of nonlinear wave type equations

In the present paper, we consider a general family of two‐dimensional wave equations, which represents a great variety of linear and nonlinear equations within the framework of the transformations of equivalence groups. We have investigated the existence problem of point transformations that lead mappings between linear and nonlinear members of particular families and determined the structure of the nonlinear terms of linearizable equations. We have also given examples about some equivalence transformations between linear and nonlinear equations and obtained exact solutions of nonlinear equations via the linear ones.     

Multidimensional nonlinear wave equations with multivalued solutions

We present the theory of breaking waves in nonlinear systems whose dynamics and spatial structure are described by multidimensional nonlinear hyperbolic wave equations. We obtain a general relation between systems of first-order quasilinear equations and nonlinear hyperbolic equations of higher orders, which, in particular, describe electromagnetic waves in a medium with nonlinear polarization of an arbitrary form. We use this approach to construct exact multivalued solutions of such equations and to study their spatial structure and dynamics. The results are generalized to a wide class of multidimensional equations such as d’Alembert equations, nonlinear Klein-Gordon equations, and nonlinear telegraph equations.     

Numerical solutions of two-dimensional nonlinear integral analysis

In this paper, the approximate solutions for two different type of two-dimensional nonlinear integral equations: two-dimensional nonlinear Volterra-Fredholm integral equations and the nonlinear mixed Volterra-Fredholm integral equations are obtained using the Laguerre wavelet method. To do this, these two-dimensional nonlinear integral equations are transformed into a system of nonlinear algebraic equations in matrix form. By solving these systems, unknown coefficients are obtained. Also, some theorems are proved for convergence analysis.Some numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the proposed method.