Results 31 to 40 of about 1,746 (107)

Algebraic Lower Bounds on the Spatial Analyticity Radius for Higher Order Nonlinear Schrödinger Equations

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
We investigate the initial value problem associated to the higher order nonlinear Schrödinger equation i∂tu+−1j+1∂x2ju=u2ju x,t≠0∈ℝ,ux,0=u0x, where j ≥ 2 is any integer, u is a complex valued function, and the initial data u0 is real analytic on ℝ and has a uniform radius of spatial analyticity σ0 in the space variable.
Tegegne Getachew, Birilew Belayneh, Betre Shiferaw, Huaiqin Wu   +3 more
wiley   +1 more source

Global well-posedness for the Gross-Pitaevskii equation with an angular momentum rotational term

, 2008
In this paper, we establish the global well-posedness of the Cauchy problem for the Gross-Pitaevskii equation with an rotational angular momentum term in the space $\Real^2$.Comment: 10 ...
Avron, Bao, Bao, Borisov, Carles, Carles, Cazenave, Gross, Hall, Keel, Landau, Madison, Madison, Matthews, Pitaevskii, Pitaevskii, Zhang   +16 more
core   +1 more source

Self-similar blow-up solutions of the four-dimensional Schrödinger-Wave system

Advances in Nonlinear Analysis
This article is primarily dedicated to the investigation of the initial value problem for the Schrödinger-wave system in dimension four. By employing self-similar transformations in conjunction with the Banach fixed-point theorem, we establish the ...
Hou Wenhe, Li Fangfang, Ma Yansheng, Zhang Dan   +3 more
doaj   +1 more source

The gauge transformation of the constrained semi-discrete KP hierarchy

, 2013
In this paper, the gauge transformation of the constrained semi-discrete KP(cdKP) hierarchy is constructed explicitly by the suitable choice of the generating functions.
Cheng, Jipeng, He, Jingsong, Li, Maohua
core   +2 more sources

Global well-posedness of some high-order focusing semilinear evolution equations with exponential nonlinearity

Advances in Nonlinear Analysis, 2018
In even space dimensions, the initial value problems for some high-order focusing semilinear evolution equations with exponential nonlinearities are considered.
Saanouni Tarek
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
doaj   +1 more source

The NLS equation in dimension one with spatially concentrated nonlinearities: the pointlike limit

, 2014
In the present paper we study the following scaled nonlinear Schr\"odinger equation (NLS) in one space dimension: \[ i\frac{d}{dt} \psi^{\varepsilon}(t) =-\Delta\psi^{\varepsilon}(t) + \frac{1}{\epsilon}V\left(\frac{x}{\epsilon}\right)|\psi^{\varepsilon}(
Cacciapuoti, C., Finco, D., Noja, D., Teta, A.   +3 more
core   +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

A Fujita-type blowup result and low energy scattering for a nonlinear Schr\"o\-din\-ger equation

, 2015
In this paper we consider the nonlinear Schr\"o\-din\-ger equation $i u_t +\Delta u +\kappa |u|^\alpha u=0$. We prove that if $\alpha
Cazenave, Thierry, Correia, Simão, Dickstein, Flávio, Weissler, Fred B.   +3 more
core   +3 more sources

Ground state solutions for magnetic Schrödinger equations with polynomial growth

Advances in Nonlinear Analysis
In this article, we investigate the following nonlinear magnetic Schrödinger equations: (−i∇+A(x))2u+V(x)u=f1(x,∣v∣2)v,(−i∇+A(x))2v+V(x)v=f2(x,∣u∣2)u,\left\{\begin{array}{l}{\left(-i\nabla +A\left(x))}^{2}u+V\left(x)u={f}_{1}\left(x,{| v| }^{2})v ...
Wu Yan, Chen Peng
doaj   +1 more source