A spectral mapping theorem and invariant manifolds for nonlinear Schrodinger equations
نویسندگان
چکیده
منابع مشابه
A Spectral Mapping Theorem and Invariant Manifolds for Nonlinear Schrodinger Equations
A spectral mapping theorem is proved that resolves a key problem in applying invariant manifold theorems to nonlinear Schrodinger type equations. The theorem is applied to the operator that arises as the linearization of the equation around a standing wave solution. We cast the problem in the context of space-dependent nonlinearities that arise in optical waveguide problems. The result is, howe...
متن کاملŠilnikov manifolds in coupled nonlinear Schrodinger equations ̈
We consider two coupled nonlinear Schrodinger equations with even, periodic boundary conditions, that are damped and ̈ ˇ quasiperiodically forced. We prove the existence of invariant manifolds with Silnikov-type dynamics that are homoclinic to a spatially independent invariant torus. Such manifolds appear to induce complex behavior in numerical experiments. q 1999 Published by Elsevier Science B...
متن کاملA note on spectral mapping theorem
This paper aims to present the well-known spectral mapping theorem for multi-variable functions.
متن کاملglobal results on some nonlinear partial differential equations for direct and inverse problems
در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
Self - Similar Solutions for Nonlinear Schrodinger Equations ∗
In this paper we study self-similar solutions for nonlinear Schrödinger equations using a scaling technique and the partly contractive mapping method. We establish the small global well-posedness of the Cauchy problem for nonlinear Schrödinger equations in some non-reflexive Banach spaces which contain many homogeneous functions. This we do by establishing some a priori nonlinear estimates in B...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 2000
ISSN: 0022-2518
DOI: 10.1512/iumj.2000.49.1838