Results 31 to 40 of about 1,815 (116)
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
wiley +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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Dynamics on resonant clusters for the quintic non linear Schr\"odinger equation [PDF]
, 2012 We construct solutions to the quintic nonlinear Schr\"odinger equation on the circle with initial conditions supported on arbitrarily many different resonant clusters.
Haus, Emanuele, Thomann, Laurent
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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
wiley +1 more source
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
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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, 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
semanticscholar +1 more source
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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