Results 31 to 40 of about 1,705 (80)

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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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
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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
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Nehari-type ground state solutions for a Choquard equation with doubly critical exponents

Advances in Nonlinear Analysis, 2020
This paper deals with the following Choquard equation with a local nonlinear perturbation:
Chen Sitong, Tang Xianhua, Wei Jiuyang
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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

Local and global well-posedness of the Maxwell-Bloch system of equations with inhomogeneous broadening

Advances in Nonlinear Analysis
The Maxwell-Bloch system of equations with inhomogeneous broadening is studied, and the local and global well-posedness of the corresponding initial-boundary value problem is established by taking advantage of the integrability of the system and making ...
Biondini Gino, Prinari Barbara, Zhang Zechuan   +2 more
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
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Nonlinear nonlocal elliptic problems in ℝ3: existence results and qualitative properties

Demonstratio Mathematica
We consider the following nonlinear nonlocal elliptic problem: −a+b∫R3∣∇ψ∣2dxΔψ+λψ=∫R3G(ψ(y))∣x−y∣αdyG′(ψ),x∈R3,-\left(a+b\mathop{\int }\limits_{{{\mathbb{R}}}^{3}}{| \nabla \psi | }^{2}{\rm{d}}x\right)\Delta \psi +\lambda \psi =\left(\mathop{\int ...
Lü Dengfeng, Dai Shu-Wei
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Effects of Brownian noise strength on new chiral solitary structures

Journal of Low Frequency Noise, Vibration and Active Control, 2023
In this paper, we investigate the nonlinear Chiral Schrödinger equation (CNLSE) in two dimensions where noise term affected randomly with time. This equation characterized some edges states of fractional-Hall Effect features in quantum.
Yousef F Alharbi, Emad K El-Shewy, Mahmoud AE Abdelrahman   +2 more
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Existence and nonexistence of normalized solutions for the Biharmonic equation with combined nonlinearities

Demonstratio Mathematica
This article is devoted to the study of the existence and nonexistence of normalized solutions for the following biharmonic Schrödinger equation with combined power-type ...
Liu Xiang, Huang Na, Lei Chunyu
doaj   +1 more source