Last edited by Maule
Saturday, May 16, 2020 | History

6 edition of The complex WKB method for nonlinear equations I found in the catalog.

The complex WKB method for nonlinear equations I

linear theory

by V. P. Maslov

  • 229 Want to read
  • 29 Currently reading

Published by Birkhäuser in Basel, Boston .
Written in English

    Subjects:
  • WKB approximation,
  • Differential equations, Linear -- Asymptotic theory,
  • Differential equations, Nonlinear -- Asymptotic theory,
  • Mathematical physics

  • Edition Notes

    Includes bibliographical references and index.

    StatementVictor P. Maslov ; translated from the Russian by M.A. Shishkova and A.B. Sossinsky.
    SeriesProgress in physics ;, v. 16, Progress in physics (Boston, Mass.) ;, v. 16.
    Classifications
    LC ClassificationsQC20.7.W53 M37 1994
    The Physical Object
    Paginationvii, 300 p. :
    Number of Pages300
    ID Numbers
    Open LibraryOL1098113M
    ISBN 103764350881, 0817650881
    LC Control Number94022799

    () Dispersion relation equation preserving FDTD method for nonlinear cubic Schrödinger equation. Journal of Computational Physics , () Spin-dipole oscillation and relaxation of coherently coupled Bose–Einstein by: equation, the diffusion equation and the wave equation, have the properties that they do. We also consider complex variable methods for solving Laplace’s equation, emphasizing their application to problems in fluid mechanics. The second part of the book is concerned with nonlinear problems and more advanced techniques.

    Bisection Method of Solving a Nonlinear Equation. After reading this chapter, you should be able to: 1. follow the algorithm of the bisection method of solving a nonlinear equation, 2. use the bisection method to solve examples of findingroots of a nonlinear equation, and 3. enumerate the advantages and disadvantages of the bisection Size: KB.   An essential graduate level text on the asymptotic analysis of ordinary differential equations, this book covers all the important methods including dominant balance, the use of divergent asymptotic series, phase integral methods, asymptotic evaluation of .

    This volume is concerned with a detailed description of the canonical operator method - one of the asymptotic methods of linear mathematical physics. The book is, in fact, an extension and continuation of the authors' works [59], [60], [65]. The basic ideas are summarized in the Introduction. The book consists of two parts. In the first, the theory of the canonical operator is develop ed. SIAM Journal on Numerical Analysis > Vol Issue 6 > Superlattice Patterns in the Complex Ginzburg–Landau Equation with Multiresonant Forcing On Fourier Time-Splitting Methods for Nonlinear Schrödinger Equations in the Semiclassical Limit. Related by:


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The complex WKB method for nonlinear equations I by V. P. Maslov Download PDF EPUB FB2

The Complex WKB Method for Nonlinear Equations I: Linear Theory (Progress in Mathematical Physics) (v. 1) Hardcover – August 1, by Victor P. Maslov (Author), M.A. Shishkova (Translator), A.B. Sossinsky (Translator) & 0 moreCited by: Eigenvalue Jacobi Mathematica eigenvector field theory instanton manifold mechanics quantum field quantum field theory quantum mechanics schrödinger equation statistics Authors and.

The Complex WKB Method for Nonlinear Equations I Linear Theory. Authors: Maslov, Victor P. Free Preview. The Complex WKB Method for Nonlinear Equations I: Linear Theory - Ebook written by Victor P. Maslov.

Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read The Complex WKB Method for Nonlinear Equations I: Linear Theory. The Complex Wkb Method for Nonlinear Equations I has 2 available editions to buy at.

The Complex WKB Method for Nonlinear Equations 1: ear Equations 1: Linear Theory. By Vc- tor P Maslov, Progress in Physics, rather than Progress in The Complex WKB Method for Nonlinear Equations /5(). WKB Approximation of the Nonlinear Schro¨dinger-Newton Equations 3 Equation (9) can be written in a different form in order to indicate the asymptotic behaviour for large r U(r) = U0 − Z r 0 xS(x)2 dx+ 1 r Z r 0 x2S(x)2 dxr−→→∞ U ∞ + I r, (12) where we only assumed the solutions to be normalizable.

In this case, both integrals. For a di erent perspective on the WKB method for the one-dimensional Schr odinger equation (from the point of view of the stationary phase approximation), see the book review by Marsden and Weinstein of the book Geometric asymptotics by Guillemin and Sternberg.

It appeared in. Wentzel-Kramers-Brillouin (WKB) Approximation •The WKB approximation is a “semiclassical calculation” in quantum mechanics in which the wave function is assumed an exponential function with amplitude and phase that slowly varies compared to the de Broglie wavelength, λ, and is then semiclassically Size: KB.

Numerical Methods I Solving Nonlinear Equations Aleksandar Donev Courant Institute, NYU1 [email protected] 1Course G / G, Fall October 14th, A. Donev (Courant Institute) Lecture VI 10/14/ 1 / 31File Size: KB. The Complex WKB Method for Nonlinear Equations I: Linear Theory. [Victor P Maslov] -- When this book was first published (in Russian), it proved to become the fountainhead of a major stream of important papers in mathematics, physics and even chemistry; indeed, it formed the basis of.

Equations and problems of narrow beam mechanics --Ch. Hamiltonian formalism of narrow beams --Ch. III. Approximate solutions of the nonstationary transport equation --Ch. Stationary Hamilton-Jacobi and transport equations --Ch. Complex Hamiltonian formalism of compact (cyclic) beams --Ch.

Canonical operators on Lagrangian manifolds with complex. Maslov, The Complex WKB Method for Nonlinear Equations. Solution interpolation method for highly oscillating hyperbolic equations In other words, here we use the same assumptions as in the nonlinear asymptotic WKB method (Pelinovsky, ; Engelbrecht et al., ; Didenkulova, ).

Books. Publishing Support. Login. Reset your password. Maslov V P Complex WKB Method in Nonlinear Equations Nauka, Moscow (in Russian) Google Scholar [7] Babitch V M and Boldyrev V S Asymptotic Methods in Problems of Short Wave Diffraction Nauka, Moscow (in Russian).

The book gives the practical means of finding asymptotic solutions to differential equations, and relates WKB methods, integral solutions, Kruskal-Newton diagrams, and boundary layer theory to one another.

The construction of integral solutions and analytic continuation are used in conjunction with. Lecture Notes on Numerical Analysis of Nonlinear Equations. This book covers the following topics: The Implicit Function Theorem, A Predator-Prey Model, The Gelfand-Bratu Problem, Numerical Continuation, Following Folds, Numerical Treatment of Bifurcations, Examples of Bifurcations, Boundary Value Problems, Orthogonal Collocation, Hopf Bifurcation and Periodic Solutions, Computing Periodic.

Then asymptotic methods of integration of such equations must be used. The WKB–Maslov method [21, 22] is one of the most advanced asymptotic methods. This work is devoted to applications of this method to the construction of asymptotic solutions of the nonlinear Fokker–Planck equation.

The nonlinear Schrödinger equation (NLSE) is a partial differential equation For the linear Schödinger equation, the Gaussian beam method, Plugging the above WKB ansatz into the NLSE/GPE and identifying real and imaginary parts, Cited by: When the phase S(x) is real (Im S(x) = 0), the method for obtaining asymptotics of this type is known in quantum mechanics as the WKB-method.

We preserve this terminology in the case Im S (x) ≥ 0 and develop the method for a wide class of problems in mathematical physics. linear algebra, and the central ideas of direct methods for the numerical solution of dense linear systems as described in standard texts such as [7], [],or[].

Our approach is to focus on a small number of methods and treat them in depth. Though this book is written in a finite-dimensional setting, we. Solve nonlinear complex equations. Follow views (last 30 days) Ed on 10 Feb Vote.

0 ⋮ Vote. Commented: Meng Li on 21 Jul Accepted Answer: Matt J. If so, this method should be much easier than to pose the equation in terms of real and complex parts. Thanks again. Matt J on 10 Feb. Buy Local Methods in Nonlinear Differential Equations: Part I, the Local Method of Nonlinear Analysis of Differential Equations: Part Ii, the Sets of an Mathematics) (English and Russian Edition) on FREE SHIPPING on qualified orders.NUMERICAL ANALYSIS USING SCILAB solving nonlinear equations Step 2: Roadmap This tutorial is composed of two main parts: the first one (Steps ) contains an introduction about the problem of solving nonlinear equations, presents some solution strategies and introduces properties and issues of such problems and Size: KB.Approximate Analytical Methods for Solving Ordinary Differential Equations (ODEs) is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to.