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On solutions of nonlinear wave equations.

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Published by Courant Institute of Mathematical Sciences, New York University in New York .
Written in English

Book details:

The Physical Object
Pagination11 p.
Number of Pages11
ID Numbers
Open LibraryOL17868040M

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  The theory of nonlinear wave equations in the absence of shocks began in the s. Despite a great deal of recent activity in this area, some major issues remain unsolved, such as sharp conditions for the global existence of solutions with arbitrary initial data, and the global phase portrait in the presence of periodic solutions and traveling waves. This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions. Publisher Summary. This chapter discusses some results on the uniqueness of solutions to systems of conservation laws of the form U t + f (U) x = 0, –∞ nonlinear mapping from R n to R chapter presents the assumption that this equation is strictly hyperbolic, that is, the Jacobian ∇f of f has n real and distinct eigenvalues: λ 1. Solitons and Nonlinear Wave Equations by R. K. Dodd (Author) ISBN ISBN X. Why is ISBN important? ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book. The digit and digit formats both work.

7{The Nonlinear Wave Equation and the Interaction of Waves MATH 22C 1. Introduction Just as the nonlinear advection equation looks the same as the linear advection equation ut+ cux = 0 except that the speed of sound cdepends on the solution u, so also the nonlinear wave equation is the linear wave equation utt c2uxx = 0 under the assumption. This monograph deals with recent advances in the study of the long-time asymptotics of large solutions to critical nonlinear dispersive equations. The first part of the monograph describes, in the context of the energy critical wave equation, the “concentration-compactness/rigidity theorem method” introduced by C. Kenig and F. Merle. Specially, for a class of nonlinear wave equations, fundamental properties of profiles of traveling wave solutions determined by some bounded orbits of the traveling wave systems are rigorously proved. Parametric conditions that guarantee the existence of the aforementioned solutions . (subscripts denote partial derivatives). This is the wave equation in one (spatial) dimension. The assumption that one can add the waves together agrees with the linearity of the wave equation; any linear combination of solutions of () is also a solution of (). A better way of deriving the wave equation is to start from physical principles.

@article{osti_, title = {Solitons and nonlinear wave equations}, author = {Dodd, Roger K and Eilbeck, J Chris and Gibbon, John D and Morris, Hedley C}, abstractNote = {A discussion of the theory and applications of classical solitons is presented with a brief treatment of quantum mechanical effects which occur in particle physics and quantum field theory. A method is proposed for obtaining traveling‐wave solutions of nonlinear wave equations that are essentially of a localized nature. It is based on the fact that most solutions are functions of a hyperbolic tangent. This technique is straightforward to use and only minimal algebra is needed to find these solutions. The method is applied to. In this article, we focus on the life span of solutions to the following system of nonlinear wave equations: in a bounded domain Ω ⊂ ℝ n with Robin and Dirichlét boundary conditions on u and v, respectively. The nonlinearities f 1(u, v) and f 2(u, v) represent strong sources of supercritical order, while g 1(u t) and g 2(v t) represent interior damping.   [Show full abstract] solutions of the KdV equation, the profiles of the intensity of the dark nonlinear waves display multi-layer ring-shapes, and can be controlled by the initial phase and the.