Stability of Periodic Solutions to Nonlinear Klein-Gordon Equations
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File Size : 21,20 MB
Release : 2012
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Page : pages
File Size : 21,20 MB
Release : 2012
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Author : Xinming Zhao
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Page : 186 pages
File Size : 48,43 MB
Release : 1996
Category : Klein-Gordon equation
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Page : 0 pages
File Size : 10,97 MB
Release : 1968
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Solutions to a nonlinear wave equation were analyzed for their stability. The wave equation is a Klein-Gordon equation with the mass replaced by the square of the wave function. This wave equation has propagating solutions which are unbounded or periodic, depending on the sign of the nonlinear term and the propagation speed which can be sub- or super-light velocity. The stability of the periodic sub-light velocity solution was investigated by the method of characteristic exponents and was found to be indifferent. Liapounoff's direct method and Sturrock's analysis of the dispersion relation combined with a WKB technique were applied to a linearized perturbation on a static solution of the field equation. The periodic solution with beta squared
Author : William Joseph Davis
Publisher :
Page : 65 pages
File Size : 14,79 MB
Release : 1968
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Solutions to a nonlinear wave equation were analyzed for their stability. The wave equation is a Klein-Gordon equation with the mass replaced by the square of the wave function. This wave equation has propagating solutions which are unbounded or periodic, depending on the sign of the nonlinear term and the propagation speed which can be sub- or super-light velocity. The stability of the periodic sub-light velocity solution was investigated by the method of characteristic exponents and was found to be indifferent. Liapounoff's direct method and Sturrock's analysis of the dispersion relation combined with a WKB technique were applied to a linearized perturbation on a static solution of the field equation. The periodic solution with beta squared
Author : Gangwei Wang
Publisher : Frontiers Media SA
Page : 192 pages
File Size : 24,1 MB
Release : 2024-08-13
Category : Science
ISBN : 2832553095
Nonlinear problems, originating from applied science that is closely related to practices, contain rich and extensive content. It makes the corresponding nonlinear models also complex and diverse. Due to the intricacy and contingency of nonlinear problems, unified mathematical methods still remain far and few between. In this regard, the comprehensive use of symmetric methods, along with other mathematical methods, becomes an effective option to solve nonlinear problems.
Author : Walter A. Strauss
Publisher : American Mathematical Soc.
Page : 106 pages
File Size : 34,29 MB
Release : 1990-01-12
Category : Mathematics
ISBN : 0821807250
The theory of nonlinear wave equations in the absence of shocks began in the 1960s. 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, based on lectures presented by the author at George Mason University in January 1989, seeks to present the sharpest results to date in this area. The author surveys the fundamental qualitative properties of the solutions of nonlinear wave equations in the absence of boundaries and shocks. These properties include the existence and regularity of global solutions, strong and weak singularities, asymptotic properties, scattering theory and stability of solitary waves. Wave equations of hyperbolic, Schrodinger, and KdV type are discussed, as well as the Yang-Mills and the Vlasov-Maxwell equations. The book offers readers a broad overview of the field and an understanding of the most recent developments, as well as the status of some important unsolved problems. Intended for mathematicians and physicists interested in nonlinear waves, this book would be suitable as the basis for an advanced graduate-level course.
Author : M. Mimura
Publisher : Elsevier
Page : 249 pages
File Size : 44,9 MB
Release : 2000-04-01
Category : Mathematics
ISBN : 0080872093
This volume contains papers covering the theory of nonlinear PDEs and the related topics which have been recently developed in Japan.
Author : Mathew A. Johnson
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Page : pages
File Size : 42,89 MB
Release : 2009
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Author : Carsten Blank
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Page : pages
File Size : 37,65 MB
Release : 2010
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Author : Marko Kostić
Publisher : Walter de Gruyter GmbH & Co KG
Page : 734 pages
File Size : 34,11 MB
Release : 2021-11-22
Category : Mathematics
ISBN : 3110763524
Covers uniformly recurrent solutions and c-almost periodic solutions of abstract Volterra integro-differential equations as well as various generalizations of almost periodic functions in Lebesgue spaces with variable coefficients. Treats multi-dimensional almost periodic type functions and their generalizations in adequate detail.