Results 21 to 30 of about 1,746 (107)
On the method of pseudopotential for Schrödinger equation with nonlocal boundary conditions
Abstract and Applied Analysis, Volume 6, Issue 6, Page 329-338, 2001., 2001 For stationary Schrödinger equation in ℝ n with the finite potential the singular pseudopotential is constructed in the form allowing us to find wave functions. The method does not require the knowledge of the explicit form of a potential and assumes only knowledge of the scattering amplitude for fixed level of energy.
Yuriy Valentinovich Zasorin
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On the instability for the cubic nonlinear Schrodinger equation
, 2007 We study the flow map associated to the cubic Schrodinger equation in space dimension at least three.
Burq +5 more
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MODIFIED SCATTERING FOR THE CUBIC SCHRÖDINGER EQUATION ON PRODUCT SPACES AND APPLICATIONS
Forum of Mathematics, Pi, 2015 We consider the cubic nonlinear Schrödinger equation posed on the spatial domain $\mathbb{R}\times \mathbb{T}^{d}$. We prove modified scattering and construct modified wave operators for small initial and final data respectively ($1\leqslant d\leqslant 4$
ZAHER HANI +3 more
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Attractors of semigroups associated with nonlinear systems for diffusive phase separation
Abstract and Applied Analysis, Volume 1, Issue 2, Page 169-192, 1996., 1996 We consider a model for diffusive phase transitions, for instance, the component separation in a binary mixture. Our model is described by two functions, the absolutete temperature θ : = θ(t, x) and the order parameter w : = w(t, x), which are governed by a system of two nonlinear parabolic PDEs.
Nobuyuki Kenmochi
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Global well-posedness on the derivative nonlinear Schr\"odinger equation revisited
, 2014 As a continuation of the previous work \cite{Wu}, we consider the global well-posedness for the derivative nonlinear Schr\"odinger equation. We prove that it is globally well-posed in energy space, provided that the initial data $u_0\in H^1(\mathbb{R ...
Wu, Yifei
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Qualitative analysis for the nonlinear fractional Hartree type system with nonlocal interaction
Advances in Nonlinear Analysis, 2021 In the present paperwe study the existence of nontrivial solutions of a class of static coupled nonlinear fractional Hartree type system. First, we use the direct moving plane methods to establish the maximum principle(Decay at infinity and Narrow region
Wang Jun
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A note on Berestycki-Cazenave's classical instability result for nonlinear Schr\"odinger equations
, 2007 In this note we give an alternative, shorter proof of the classical result of Berestycki and Cazenave on the instability by blow-up for the standing waves of some nonlinear Schr\"odinger ...
Coz, Stefan Le
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Local well-posedness of nonlinear dispersive equations on modulation spaces
, 2007 By using tools of time-frequency analysis, we obtain some improved local well-posedness results for the NLS, NLW and NLKG equations with Cauchy data in modulation spaces $M{p, 1}_{0,s}$.Comment: 11 ...
Bényi, Árpád, Okoudjou, Kasso A.
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Journal of Function SpacesMSC2020 Classification: 35G25, 35Q55, 42B35 ...
Long Xiao, Ting Chen
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International Journal of Differential Equations, Volume 2025, Issue 1, 2025.The mathematical models of problems that arise in many branches of science are nonlinear equations of evolution (NLEE). For this reason, NLEE have served as a language in formulating many engineering and scientific problems. Although the origin of nonlinear evolution equations dates back to ancient times, significant developments have been made in ...
Murat Koparan, Salim A. Messaoudi
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