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pro vyhledávání: '"35Q55"'
Autor:
Colin, Mathieu, Watanabe, Tatsuya
This paper is devoted to the study of the nonlinear Schr\"odinger-Poisson system with a doping profile. We are interested in the existence of stable standing waves by considering the associated $L^2$-minimization problem. The presence of a doping pro
Externí odkaz:
http://arxiv.org/abs/2409.01842
In this article, we study the long-time dynamics of threshold solutions for the focusing energy-critical inhomogeneous Schr\"odinger equation and classify the corresponding threshold solutions in dimensions $d=3,4,5$. We first show the existence of s
Externí odkaz:
http://arxiv.org/abs/2409.00073
Autor:
Jenkins, Robert, Tovbis, Alexander
In this paper we approximate the thermodynamic limit of finite-gap solutions to any integrable equations in the focusing NLS hierarchy (fNLS, mKdV, ...) with an associated multisoliton solutions using the Riemann-Hilbert Problem approach. Moreover, w
Externí odkaz:
http://arxiv.org/abs/2408.13700
Autor:
Vassilev, Katja D.
Although wave kinetic equations have been rigorously derived in dimension $d \geq 2$, both the physical and mathematical theory of wave turbulence in dimension $d = 1$ is less understood. Here, we look at the one-dimensional MMT (Majda, McLaughlin, a
Externí odkaz:
http://arxiv.org/abs/2408.13693
The aim of this paper is investigating the existence of at least one nontrivial bounded solution of the new asymptotically ``linear'' problem \[ \left\{ \begin{array}{ll} - {\rm div} \left[\left(A_0(x) + A(x) |u|^{ps}\right) |\nabla u|^{p-2} \nabla u
Externí odkaz:
http://arxiv.org/abs/2408.12954
Autor:
Kim, Taegyu, Kwon, Soonsik
We consider soliton resolution for the Calogero--Moser derivative nonlinear Schr\"odinger equation (CM-DNLS). A rigorous PDE analysis of (CM-DNLS) was recently initiated by G\'erard and Lenzmann, who demonstrated its Lax pair structure. Additionally,
Externí odkaz:
http://arxiv.org/abs/2408.12843
Autor:
Alejo, Miguel Á., Corcho, Adán J.
In this work, a rigorous proof of the nonexistence of breather solutions for NLS equations is presented. By using suitable virial functionals, we are able to characterize the nonexistence of breather solutions, different from standing waves, by only
Externí odkaz:
http://arxiv.org/abs/2408.09862
Autor:
Noguera, Norman
In this work we consider a system of nonlinear Schr\"odinger equations whose nonlinearities satisfy a power-type-growth. First, we prove that the Cauchy problem is local and global well-posedness in $L^2$ and $H^1$. Next, we establish the existence o
Externí odkaz:
http://arxiv.org/abs/2408.09045
We deal with the $n$-dimensional nonlinear Schr\"{o}dinger equation (NLSE) with a cubic nonlocal nonlinearity and an anti-Hermitian term, which is widely used model for the study of open quantum system. We construct asymptotic solutions to the Cauchy
Externí odkaz:
http://arxiv.org/abs/2408.08532
Autor:
Albert, John, Arbunich, Jack
We consider the stability of bound-state solutions of a family of regularized nonlinear Schr\"odinger equations which were introduced by Dumas, Lannes and Szeftel as models for the propagation of laser beams. Among these bound-state solutions are gro
Externí odkaz:
http://arxiv.org/abs/2408.08279