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Monday, February 10, 2020 | History

13 edition of Global solutions of nonlinear Schrödinger equations found in the catalog.

Global solutions of nonlinear Schrödinger equations

  • 90 Want to read
  • 15 Currently reading

Published by American Mathematical Society in Providence, R.I .
Written in English

    Subjects:
  • Schrödinger equation,
  • Differential equations, Partial -- Numerical solutions,
  • Nonlinear theories

  • Edition Notes

    Includes bibliographical references and index.

    StatementJ. Bourgain.
    SeriesAmerican Mathematical Society colloquium publications -- v. 46, Colloquium publications (American Mathematical Society) -- v. 46.
    Classifications
    LC ClassificationsQC174.26.W28 B68 1999
    The Physical Object
    Paginationviii, 182 p. :
    Number of Pages182
    ID Numbers
    Open LibraryOL15628991M
    ISBN 100821819194
    ISBN 109780821819197
    LC Control Number99013066
    OCLC/WorldCa40869670

    Abstract and Applied Analysis The proof that a finite-time singularity can occur in Eq. Shea-Brown Stability. In the direct problem, the first step is to construct eigenfunction solutions of the associated linear problem. Dong and S-J. Ma and Lee [ 5 ] proposed the transformed rational function method for solving the -dimensional Jimbo-Miwa equation and obtained exact solutions.

    Complex Analysis and Operator Theory One can also consider discretizations of vector NLS equations, both integrable and nonintegrable. On the pointwise decay estimate for the wave equation with compactly supported forcing term. As a result, Jacobi elliptic function solution, hyperbolic function solution, trigonometric function solution, and rational solution with parameters are obtained successfully. As a result, most long-distance optical fiber submarine systems today are dispersion-managed.

    Ma [ 7 ] introduced a class of bilinear differential operators which describe generalized bilinear differential equations and discussed their links with the Bell polynomial. Global solution and decay rate for a reduced gravity two and a half layer model. As a result, Jacobi elliptic function solution, hyperbolic function solution, trigonometric function solution, and rational solution with parameters are obtained successfully. Funkcialaj Ekvacioj Tokyo, Sec. Google Scholar [HP] E.


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Global solutions of nonlinear Schrödinger equations by Jean Bourgain Download PDF Ebook

Advances in Mathematical Physics The reader is referred to [ 12324 ] and the references therein. Global well posedness for the ghost effect system. Applicable Analysis Fiber nonlinearity is due to the so-called Kerr effect, i.

Zakharov, Collapse of Langmuir waves, Sov. Figure 7: Dispersion managed Ti: sapphire laser system. Both the direct and the inverse problem make use of the first operator in the Lax pair, so-called scattering problem, while the time evolution is determined by the second operator in the Lax pair.

For example, in a two-step DM system, between every two optical amplifiers whose spacing is usually between 40 and km one has a fiber with one dispersion sign that is connected to another fiber with the opposite dispersion sign.

Crossref Escape dynamics in the discrete repulsive model.

Travelling Wave Solutions for Nonlinear Schrödinger Equation with a Higher

Chinese Annals of Mathematics, Series B In more than one dimension, the equation is not integrable, it allows for a collapse and wave turbulence.

Forum of Mathematics, Pi 3. The paper by Eilbeck et al was the first to point out the universal nature of the discrete NLS equation, and reported a number of applications, especially for periodic solutions with small periods. Mathematical Physics, This set forth the experimental foundations of computation with solitons.

On the pointwise decay estimate for the wave equation with compactly supported forcing term. Birmingham ConferenceNorth Holland Kuznetsov Conjugate maps. Figure 6: Classical and DM solitons.

Journal of Hyperbolic Differential Equations Moreover, it presents selected numerical methods for solving stochastic point kinetic equations in nuclear reactor dynamics by using Euler—Maruyama and strong-order Taylor numerical methods.

SIAM Journal on Mathematical Analysis

Reviews of Modern Physics This leads to a system of equations that describes the nonlocal-nonlinear coupling between a dynamic field that is associated with the first harmonic with a "cascaded" effect from the second harmonicand a static field that is associated with the mean term i.global existence and blow up of solutions for Cauchy problem of Eq.

(). Especially, in this paper we find an interesting phenomenon that maybe the solution of the inhomogeneous nonlinear Schrödinger equation () blows up when t →∞, which does not appear in the homogeneous case of Eq. () in [5,18,19]. At last using the sharp.

Global solutions of nonlinear Schrödinger equations

Mar 01,  · AbstractThe Cauchy problem of Global solutions of nonlinear Schrödinger equations book Schrödinger equation with a harmonic potential for describing the attractive Bose-Einstein condensate under the magnetic trap is considered. We give some sufficient conditions of global existence and finite time blow up of solutions by introducing a family of potential wells.

Some different sharp conditions for global existence, and some invariant sets Author: Mingyou Zhang, Salik Ahmed. All Book Search results » Bibliographic information. Title: Global Solutions of Nonlinear Schrödinger Equations, Volume 46 Volume 46 of American Mathematical Society colloquium publications Volume 46 of Colloquium Publications - American Mathematical Society Issue 46 of Colloquium publications Global solutions of nonlinear Schrödinger.Exact Solutions > Nonlinear Partial Differential Equations > Second-Order Pdf Partial Differential Equations > Nonlinear Schrodinger Equation (Schrodinger Equation)¨ Schrodinger, equation, equations, nonlinear, general form, exact solutions Created Date.THE DISCRETE NONLINEAR SCHRODINGER EQUATION˜ to write down, see the book by Faddeev and Takhtajan37 for details.

Both the AL model and the Izergin{Korepin models have the advantage of being Stationary solutions of the DNLS or DST equations are .Chapters 1 and 2 of this thesis deal with ebook and lifespans of solutions for the linear and nonlinear Dirac equations.

We establish local and almost global existence results as well as ill-posedness below the critical regularity, H ̇ 1/tjarrodbonta.com: David C. Webb.