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pro vyhledávání: '"35q55"'
The regularity of solutions to the stochastic nonlinear wave equation plays a critical role in the accuracy and efficiency of numerical algorithms. Rough or discontinuous initial conditions pose significant challenges, often leading to a loss of accu
Externí odkaz:
http://arxiv.org/abs/2412.14644
We study the quantum many-body dynamics of a Bose-Einstein condensate (BEC) on the lattice in the mean-field regime. We derive a local enhancement of the mean-field approximation: At positive distance $\rho>0$ from the initial BEC, the mean-field app
Externí odkaz:
http://arxiv.org/abs/2412.13868
Autor:
Jeong, Uihyeon, Kim, Taegyu
We consider the Calogero--Moser derivative nonlinear Schr\"odinger equation (CM-DNLS), an $L^2$-critical nonlinear Schr\"odinger type equation enjoying a number of numerous structures, such as nonlocal nonlinearity, self-duality, pseudo-conformal sym
Externí odkaz:
http://arxiv.org/abs/2412.12518
We prove that nonlinear Schr\"odinger equations on the circle, without external parameters, admits plenty of almost periodic solutions. Indeed, we prove that arbitrarily close to most of the finite dimensional KAM tori constructed by Kuksin--Poschel
Externí odkaz:
http://arxiv.org/abs/2412.11845
In this paper, we investigate the global well-posedness and scattering theory for the defocusing nonlinear Schr\"odinger equation $iu_t + \Delta_\Omega u = |u|^\alpha u$ in the exterior domain $\Omega$ of a smooth, compact and strictly convex obstacl
Externí odkaz:
http://arxiv.org/abs/2412.13215
In this article, we study the existence and asymptotic properties of prescribed mass standing waves for the rotating dipolar Gross-Pitaevskii equation with a harmonic potential in the unstable regime. This equation arises as an effective model descri
Externí odkaz:
http://arxiv.org/abs/2412.09890
We study log-correlated Gibbs measures on the $d$-dimensional torus with weakly interacting focusing quartic potentials whose coupling constants tend to $0$ as we remove regularization. In particular, we exhibit a phase transition for this model by i
Externí odkaz:
http://arxiv.org/abs/2412.09790
Autor:
Höfer, Fabian, Nikov, Niko A.
We prove logarithmic growth bounds on Sobolev norms of the focusing mass-critical NLS and gKdV equations on the torus, which hold almost surely under the focusing Gibbs measure with optimal mass threshold constructed by Oh, Sosoe, and Tolomeo. More p
Externí odkaz:
http://arxiv.org/abs/2412.08630
We investigate the decay estimates of global solutions for a class of one-dimensional inhomogeneous nonlinear Schr\"odinger equations. While most existing results focus on spatial dimensions $d\geq2$, the decay properties in one dimension remain less
Externí odkaz:
http://arxiv.org/abs/2412.08272
Autor:
Miller, Ian
In this article we obtain new scattering and blow-up solutions for intercritical focusing nonlinear Schr\"{o}dinger equations (NLS) above the ground state mass-energy threshold. The main focus of this article is the establishment of some solutions wi
Externí odkaz:
http://arxiv.org/abs/2412.06962