On the solitonic wave structures and stability analysis of the stochastic nonlinear Schrödinger equation with the impact of multiplicative noise

H Zulfiqar, A Aashiq, KU Tariq, H Ahmad, B Almohsen… - Optik, 2023 - Elsevier
The nonlinear Schrödinger equation (NLSE) is a fundamental and significant physical model
that plays a crucial role in demonstrating the dynamics of optical solitons in the theory optical …

Ergodic results for the stochastic nonlinear Schrödinger equation with large damping

Z Brzeźniak, B Ferrario, M Zanella - Journal of Evolution Equations, 2023 - Springer
Ergodic results for the stochastic nonlinear Schrödinger equation with large damping | Journal
of Evolution Equations Skip to main content SpringerLink Log in Menu Find a journal Publish …

Martingale solutions for the stochastic nonlinear Schrödinger equation in the energy space

Z Brzeźniak, F Hornung, L Weis - Probability Theory and Related Fields, 2019 - Springer
We consider a stochastic nonlinear Schrödinger equation with multiplicative noise in an
abstract framework that covers subcritical focusing and defocusing Stochastic NLSE in H^ 1 …

Scattering for stochastic nonlinear Schrödinger equations

S Herr, M Röckner, D Zhang - Communications in Mathematical Physics, 2019 - Springer
We study the scattering behavior of global solutions to stochastic nonlinear Schrödinger
equations with linear multiplicative noise. In the case where the quadratic variation of the …

Stochastic logarithmic Schrödinger equations: energy regularized approach

J Cui, L Sun - SIAM Journal on Mathematical Analysis, 2023 - SIAM
In this paper, we prove the global existence and uniqueness of the solution of the stochastic
logarithmic Schrödinger (SlogS) equation driven by either additive noise or multiplicative …

Global well-posedness for the defocussing mass-critical stochastic nonlinear Schrödinger equation on ℝ at L2 regularity

C Fan, W Xu - Analysis & PDE, 2021 - msp.org
We prove global existence and stability of the solution to the mass-critical stochastic
nonlinear Schrödinger equation in d= 1 with L ω∞ L x 2 initial data. Our construction starts …

Solitary waves in a stochastic parametrically forced nonlinear Schr\" odinger equation

MV Gnann, RWS Westdorp, J van Winden - arXiv preprint arXiv …, 2024 - arxiv.org
We study a parametrically forced nonlinear Schr\" odinger (PFNLS) equation, driven by
multiplicative translation-invariant noise. We show that a solitary wave in the stochastic …

Stochastic nonlinear Schrödinger equations on tori

K Cheung, R Mosincat - … and Partial Differential Equations: Analysis and …, 2019 - Springer
We consider the stochastic nonlinear Schrödinger equations (SNLS) posed on d-
dimensional tori with either additive or multiplicative stochastic forcing. In particular, for the …

Optimal bilinear control of stochastic nonlinear Schrödinger equations: mass-(sub) critical case

D Zhang - Probability Theory and Related Fields, 2020 - Springer
We study optimal control problems for stochastic nonlinear Schrödinger equations in both
the mass subcritical and critical case. For general initial data of the minimal L^ 2 L 2 …

The stochastic nonlinear Schrödinger equations driven by pure jump noise

J Wang, J Zhai, J Zhu - Statistics & Probability Letters, 2023 - Elsevier
In this paper, we establish the existence and uniqueness of solutions of stochastic nonlinear
Schrödinger equations with additive jump noise in L 2 (R d). Our results cover all either …