Variational Solution of Stochastic Schrödinger Equations With Power-Type Nonlinearity

DOI10.1080/07362994.2015.1029133zbMath1325.60109OpenAlexW1551188811MaRDI QIDQ3448334

Diana Keller, Hannelore Breckner

Publication date: 23 October 2015

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07362994.2015.1029133

zbMATH Keywords

Galerkin methodvariational solutionpower-type nonlinearitystochastic nonlinear Schrödinger equationmultiplicative Gaussian noise

Mathematics Subject Classification ID

Gaussian processes (60G15) NLS equations (nonlinear Schrödinger equations) (35Q55) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items

Effective wave factorization for a stochastic Schrödinger equation ⋮ A stochastic nonlinear Schrödinger problem in variational formulation ⋮ Averaging principle for multiscale stochastic fractional Schrödinger equation ⋮ Effective approximation for a nonlocal stochastic Schrödinger equation with oscillating potential ⋮ Optimal control results for a class of stochastic Schrödinger equations ⋮ The stochastic nonlinear Schrödinger equation in unbounded domains and non-compact manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• 1D quintic nonlinear Schrödinger equation with white noise dispersion
• On the well-posedness for stochastic Schrödinger equations with quadratic potential
• Stochastic nonlinear Schrödinger equations with linear multiplicative noise: rescaling approach
• The nonlinear Schrödinger equation with white noise dispersion
• Classical solutions of nonlinear Schrödinger equations
• Classical solutions of nonlinear Schrödinger equations in higher dimensions
• On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
• Time dependent nonlinear Schrödinger equations
• On an initial-boundary value problem for the nonlinear Schrödinger equation
• Existence and uniqueness of global solutions of nonlinear Schrödinger equations on \(\mathbb{R}^ 2\)
• On a type of stochastic differential equations driven by countably many Brownian motions
• A stochastic nonlinear Schrödinger equation with multiplicative noise
• Stabilization of solitons of the multidimensional nonlinear Schrödinger equation: matter-wave breathers
• Basic properties of nonlinear stochastic Schrödinger equations driven by Brownian motions
• A note on stochastic Schrödinger equations with fractional multiplicative noise
• Stationary Conjugation of Flows for Parabolic SPDEs with Multiplicative Noise and Some Applications
• On smooth solutions to the initial-boundary value problem for the nonlinear schrödinger equation in two space dimensions
• The cauchy problem for the critical nonlinear Schrödinger equation in Hs
• Local Exact Controllability and Stabilizability of the Nonlinear Schrödinger Equation on a Bounded Interval
• Equations de Schrödinger non linéaires en dimension deux
• Über Näherungsverfahren zur Lösung der nichtlinearen SCHRÖDINGER-Gleichung
• Nonlinear Schrödinger evolution equations
• The Stochastic Characteristics Method Applied to a Stochastic Schrödinger Equation
• The Stochastic Nonlinear Schrödinger Equation inH¹
• Stochastic Nonlinear Equations of Schrödinger Type
• REGULARITY OF SOLUTIONS TO LINEAR STOCHASTIC SCHRÖDINGER EQUATIONS
• The Nonlinear Schrödinger Equation with Combined Power-Type Nonlinearities