Results 31 to 40 of about 1,785 (116)
On an infinite sequence of invariant measures for the cubic nonlinear Schrödinger equation
International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 7, Page 375-394, 2001., 2001 We consider the Cauchy problem periodic in the spatial variable for the usual cubic nonlinear Schrödinger equation and construct an infinite sequence of invariant measures associated with higher conservation laws for dynamical systems generated by this problem on appropriate phase spaces.
Peter E. Zhidkov
wiley +1 more source
Perturbation results for some nonlinear equations involving fractional operators [PDF]
, 2012 By using a perturbation technique in critical point theory, we prove the existence of solutions for two types of nonlinear equations involving fractional differential operators.Comment: 14 ...
Secchi, Simone
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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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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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L^2-concentration for a coupled nonlinear Schrödinger system
Differential Equations & Applications, 2019 In this work we adapt Bourgain’s ideas in [?] to a coupled system and we prove the L2 concentration of blow-up solutions for two-coupled nonlinear Schrödinger equations at critical dimension. Mathematics subject classification (2010): 35A01, 35Q55.
X. Carvajal, P. Gamboa
semanticscholar +1 more source
Blow-up for self-interacting fractional Ginzburg-Landau equation
, 2017 The blow-up of solutions for the Cauchy problem of fractional Ginzburg-Landau equation with non-positive nonlinearity is shown by an ODE argument. Moreover, in one dimensional case, the optimal lifespan estimate for size of initial data is obtained ...
Fujiwara, Kazumasa +2 more
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Normalized solutions for a class of scalar field equations involving mixed fractional Laplacians
Advanced Nonlinear Studies, 2022 The purpose of this article is to establish sharp conditions for the existence of normalized solutions to a class of scalar field equations involving mixed fractional Laplacians with different orders.
Luo Tingjian, Hajaiej Hichem
doaj +1 more source
On the derivation of the wave kinetic equation for NLS
Forum of Mathematics, Pi, 2021 A fundamental question in wave turbulence theory is to understand how the wave kinetic equation describes the long-time dynamics of its associated nonlinear dispersive equation.
Yu Deng, Zaher Hani
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, 2016 In this paper, the F-expansion method has been used to find several types of exact solutions of the higher-order nonlinear Schrödinger (HONLS) equation with cubic-quintic nonlinearities, self-steeping and self-frequency shift effects which describes the ...
M. M. Hassan +2 more
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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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