Showing papers on "Nonlinear system published in 1979"

Topological degree methods in nonlinear boundary value problems

Abstract: Introduction Suggestions for the readerSuggestions for the reader Fredholm mappings of index zero and linear boundary value problems Degree theory for some classes of mappings Duality theorems for several fixed point operators associated to periodic problems for ordinary differential equations Existence theorems for equations in normed spaces Boundary value problems for second order nonlinear vector differential equations Periodic solutions of ordinary differential equations with one-sided growth restrictions Bound sets for functional differential equations The index of isolated zeros of some mappings Bifurcation theory Periodic solutions of autonomous ordinary differential equations around an equilibrium References.

Estimation theory with applications to communications and control

Abstract: : Much current interest in the areas of communication and control is devoted to a study of estimation theory. This text provides a comprehensive treatment of estimation theory which should be suitable for graduate level engineers. There are nine chapters in the text: Introduction to Estimation Theory, Review of Probability Theory and Random Variables, Stochast Processes, Gauss-Markov Processes and Stochastic Differential Equations, Decision Theory, Basic Estimation Theory, The Optimum Linear Filter, Extensions of the Optimum Linear Filter, Nonlinear Estimation. (Author)

Isobaric volume and enthalpy recovery of glasses. II. A transparent multiparameter theory

Abstract: A multiordering parameter model for glass-transition phenomena has been developed on the basis of nonequilibrium thermodynamics. In this treatment the state of the glass is determined by the values of N ordering parameters in addition to T and P; the departure from equilibrium is partitioned among the various ordering parameters, each of which is associated with a unique retardation time. These times are assumed to depend on T, P, and on the instantaneous state of the system characterized by its overall departure from equilibrium, giving rise to the well-known nonlinear effects observed in volume and enthalpy recovery. The contribution of each ordering parameter to the departure and the associated retardation times define the fundamental distribution function (the structural retardation spectrum) of the system or, equivalently, its fundamental material response function. These, together with a few experimentally measurable material constants, completely define the recovery behavior of the system when subjected to any thermal treatment. The behavior of the model is explored for various classes of thermal histories of increasing complexity, in order to simulate real experimental situations. The relevant calculations are based on a discrete retardation spectrum, extending over four time decades, and on reasonable values of the relevant material constants in order to imitate the behavior of polymer glasses. The model clearly separates the contribution of the retardation spectrum from the temperature-structure dependence of the retardation times which controls its shifts along the experimental time scale. This is achieved by using the natural time scale of the system which eliminates all the nonlinear effects, thus reducing the response function to the Boltzmann superposition equation, similar to that encountered in the linear viscoelasticity. As a consequence, the system obeys a rate (time) -temperature reduction rule which provides for generalization within each class of thermal treatment. Thus the model establishes a rational basis for comparing theory with experiment, and also various kinds of experiments between themselves. The analysis further predicts interesting features, some of which have often been overlooked. Among these are the impossibility of extraction of the spectrum (or response function) from experiments involving cooling from high temperatures at finite rate; and the appearance of two peaks in the expansion coefficient, or heat capacity, during the heating stage of three-step thermal cycles starting at high temperatures. Finally, the theory also provides a rationale for interpreting the time dependence of mechanical or other structure-sensitive properties of glasses as well as for predicting their long-range behavior.

Two‐dimensional lumps in nonlinear dispersive systems

Abstract: Two‐dimensional lump solutions which decay to a uniform state in all directions are obtained for the Kadomtsev–Petviashvili and a two‐dimensional nonlinear Schrodinger type equation. The amplitude of these solutions is rational in its independent variables. These solutions are constructed by taking a ’’long wave’’ limit of the corresponding N‐soliton solutions obtained by direct methods. The solutions describing multiple collisions of lumps are also presented.

Compensation for channel dispersion by nonlinear optical phase conjugation.

Abstract: It is proposed that the process of nonlinear optical phase conjugation can be utilized to compensate for channel dispersion and hence to correct for temporal pulse broadening. Specifically, a four-wave nonlinear interaction is shown to achieve pulse renarrowing. Spectral bandwidth constraints of the input pulse are presented for typical phase-conjugate interaction parameters.

The Initial Value Problem for the Equations of Motion of compressible Viscous and Heat-conductive Fluids.

Abstract: : The initial value problem associated with the equations of motion for isotropic Newtonian fluids is investigated. The fluids are compressible, viscous and heat-conductive. It is proved that there exists a unique global solution in time, for the small initial data, and the solution has the decay rate of (1 + t) to 3/4 power as t approaches positive infinity. The motions of compressible, viscous and heat-conductive fluids are described by a system of partial differential equations which is of hyperbolic-parabolic type and highly nonlinear. One of the first mathematical problems associated with this system is the initial value problem. We obtain the existence of a a unique smooth global solution in time for the initial value problem and also the decay rate of the solution as time tends to infinity.

New integrable nonlinear evolution equations

Abstract: A new series of integrable nonlinear evolution equations is presented. The equations are novel in the sense that the nonlinear terms have saturation effects. It is shown that the equations have an infinite number of conservation laws and can be expressed in the Hamiltonian form.

Laminar boundary layer on an impulsively started rotating sphere

Abstract: The problem of determining the development with time of the flow of a viscous incompressible fluid outside a rotating sphere is considered The sphere is started impulsively from rest to rotate with constant angular velocity about a diameter The motion is governed by a coupled set of three nonlinear time‐dependent partial differential equations which are solved by first employing the semi‐analytical method of series truncation to reduce the number of independent variables by one and then solving numerically a finite set of partial differential equations in one space variable and the time The calculations have been carried out on the assumption that the Reynolds number is very large The physical properties of the flow are calculated as functions of the time and compared with existing solutions for large and small times A radial jet is found to develop with time near the equator of the sphere as a consequence of the collision of the boundary layers

Solitons in Action

Abstract: Karl Lonngren and Alwyn Scott (eds) 1978 New York: Academic xiii + 300 pp price £9.75 Nonlinear partial differential equations, such as the sine-Gordon, Korteweg–de Vries or nonlinear Schrodinger equations, may be familiar to mathematicians but their remarkable soliton-bearing properties ought to be better known by the scientific community. This book is a record of a workshop in 1977 with this view in mind.

Algorithm 540: PDECOL, General Collocation Software for Partial Differential Equations [D3]

Abstract: PDECOL, new computer software package for numerically solving coupled systems of nonlinear partial differential equations (PDE's) in one space and one time dimension, is discussed. The package implements finite element collocation methods based on piecewise polynomials for the spatial discretization techniques. The time integration process is then accomplished by widely acceptable procedures that are generalizations of the usual methods for treating time-dependent partial differental equations. PDECOL is unique because of its flexibiility both in the class of problems it addresses and in the variety of methods it provides for use in the solution process. High-order methods (as well as low-order ones) are readily available for use in both the spatial and time discretization procedures. The time integration methods used feature automatic time step size and integration formula order selection so as to solve efficiently the problem at hand and yet achieve a user-specific time integration error level. PDECOL consists of a collection of 19 subroutines written in reasonably standard Fortran, and therefore is quite portable. No special hardware features are required. PDECOL is designed to solve broad classes of difficult systems of partial differential equations that descrobe physical processes. 4 figures, 1 table. (RWR)

A generalization of inverse scattering method

Abstract: A new scheme of the inverse scattering method is proposed. As an illustration of novel feature of our scheme, the set of fundamental equations has been presented for a generalized nonlinear Schrodinger equation, of which nonlinear terms are composed of a usual cubic nonlinear term and a derivative cubic nonlinear term.

Modeling and Performance Evaluation of Nonlinear Satellite Links-A Volterra Series Approach

Abstract: An analytical solution to the problem of modeling bandpass nonlinear channels and evaluating the performance of digital communication systems operating on them is presented. A method based on a Volterra series representation of the overall channel is first proposed, which allows one to extend to nonlinearities with memory the well-known concepts of complex envelope of bandpass signals and low-pass equivalent of bandpass linear systems. The general results previously mentioned are then applied to digital satellite communication systems operating over nonlinear channels. The effect of a nonlinear amplifier located in the satellite is considered, in combination with that of transmitting and receiving filters located in the Earth stations. In addition, both uplink and downlink noise are taken into account. Basic advantages of this approach are the generality it offers to the analysis and the fact that it allows accurate evaluation of the error probability in a short computer time.

Invertibility of Nonlinear Control Systems

Abstract: This paper gives necessary and sufficient conditions for the invertibility of nonlinear control systems of the form $\dot x = A(x) + uB(x)$; $y = c(x)$, where the state space is a real analytic manifold. For invertible systems we construct nonlinear inverse systems. These results are used to study the question of functional controllability for nonlinear systems. The class of real analytic functions which can appear as outputs of a given nonlinear system is described, and a prefilter is constructed to generate the required control.

Numerical computation of the Schwarz-Christoffel transformation

Abstract: A program is described which computes Schwarz–Christoffel transformations that map the unit disk conformally onto the interior of a bounded or unbounded polygon in the complex plane. The inverse map is also computed. The computational problem is approached by setting up a nonlinear system of equations whose unknowns are essentially the “accessory parameters” $z_k $. This system is then solved with a packaged subroutine.New features of this work include the evaluation of integrals within the disk rather than along the boundary, making possible the treatment of unbounded polygons; the use of a compound form of Gauss–Jacobi quadrature to evaluate the Schwarz–Christoffel integral, making possible high accuracy at reasonable cost; and the elimination of constraints in the nonlinear system by a simple change of variables.Schwarz–Christoffel transformations may be applied to solve the Laplace and Poisson equations and related problems in two-dimensional domains with irregular or unbounded (but not curved or multiply connected) geometries. Computational examples are presented. The time required to solve the mapping problem is roughly proportional to $N^3 $, where N is the number of vertices of the polygon. A typical set of computations to 8-place accuracy with $N \leqq 10$ takes 1 to 10 seconds on an IBM 370/168.

The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems

Abstract: One of the most powerful methods for studying periodic solutions In autonomous nonlinear systems is the theory which has developed from a proof by Hopf. He showed that oscillations near an equilibrium point can be understood by looking at the eigenvalues of the linearized equations for perturbations from equilibrium, and at certain crucial derivatives of the equations. A good deal of work has been done recently on this theory and the present paper summarizes recent results, presents some new ones, and shows how they can be used to study almost sinusoidal oscillations in nonlinear circuits and systems. The new results are a proof of the basic part of the Hopf theorem using only elementary methods, and a graphical interpretation of the theorem for nonlinear multiple-loop feedback systems. The graphical criterion checks the Hopf conditions for the existence of stable or unstable periodic oscillations. Since it is reminiscent of the generalized Nyquist criterion for linear systems, our graphical procedure can be interpreted as the frequencydomain version of the Hopf bifurcation theorem.

Equations d'évolution abstraites non linéaires de type parabolique

Abstract: We study abstract non linear parabolic equations by linearization and give examples to partial differential equations.

Soliton Evolution in the Presence of Perturbation

Abstract: A perturbation theory for nonlinear waves based on the inverse scattering method is presented. The theory is applied to the description of soliton evolution in the presence of permanent perturbation. It is shown that small perturbation leads to three main effects: (i) a slow change of soliton parameters; (ii) a deformation of its shape (iii) formation of a soliton tail which is a small amplitude wave packet with growing length. All these effects are investigated in detail for the Korteweg-de Vries, modified Korteweg-de Vries and nonlinear Schr?dinger equations to which perturbation terms of general form are added. It is show, in particular, that for the last equation, in contrast to the previous two, the tails do not appear for perturbations of a very broad type.

Ion Acoustic Solitons in a Plasma: A Review of their Experimental Properties and Related Theories

Abstract: A review of experiments and theories on ion acoustic solitons is presented. Taking into account quadratic nonlinearity in the fluid equations leads to the Korteweg-de Vries (KdV) equation which predicts the existence of solitons. Experimental confirmation of their existence came with the availability of plasmas with large Te/Ti which allows us to minimize damping. However, the experimental datas on the dependency of Mach number vs. soliton amplitude clearly shows a discrepancy with the prediction of the KdV equation. The recent theories do include the effects of finite ion temperature and those due to the trapped electron population. The inclusion of nonlinearity of order higher than quadratic leads to the notion of dressed solitons the dynamic of which has been studied numerically. A discussion of other nonlinear equations describing ion acoustic waves will also be presented.