Madelung, Gross-Pitaevskii and Korteweg
arXiv:1111.4670 · doi:10.1088/0951-7715/25/10/2843
Abstract
This paper surveys various aspects of the hydrodynamic formulation of the nonlinear Schrodinger equation obtained via the Madelung transform in connexion to models of quantum hydrodynamics and to compressible fluids of the Korteweg type.
32 pages
References in corpus (6)
- On the Finite Energy Weak Solutions to a System in Quantum Fluid Dynamics
- Travelling waves for the Gross-Pitaevskii equation II
- The Quantum Hydrodynamics system in two space dimensions
- Orbital stability of the black soliton to the Gross-Pitaevskii equation
- WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity
- Instabilities for supercritical Schrödinger equations in analytic manifolds
Cited by in corpus (23)
- Universal dynamics for the defocusing logarithmic Schrodinger equation
- Global well-posedness of the Euler-Korteweg system for small irrotational data
- On Fourier time-splitting methods for nonlinear Schrodinger equations in the semi-classical limit
- Quantum turbulence simulations using the Gross-Pitaevskii equation: high-performance computing and new numerical benchmarks
- Finite time extinction for nonlinear Schrodinger equation in 1D and 2D
- Rankine--Hugoniot conditions for fluids whose energy depends on space and time derivatives of density
- Small energy traveling waves for the Euler-Korteweg system
- Recent results for the Landau-Lifshitz equation
- An asymptotic preserving scheme based on a new formulation for NLS in the semiclassical limit
- Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System
- Rigidity results in generalized isothermal fluids
- Exploring Bifurcations in Bose-Einstein Condensates via Phase Field Crystal Models
- Stability theory for difference approximations of some dispersive shallow water equations and application to thin film flows
- Monokinetic solutions to a singular Vlasov equation from a semiclassical perspective
- Local weak solutions to a Navier-Stokes-nonlinear-Schrödinger model of superfluidity
- WKB analysis of the Logarithmic Nonlinear Schrodinger Equation in an analytic framework
- WKB analysis of generalized derivative nonlinear Schrodinger equations without hyperbolicity
- Ginzburg-Landau relaxation for harmonic maps on planar domains into a general compact vacuum manifold
- Small-data global existence of solutions for the Pitaevskii model of superfluidity
- On the mass transfer in the 3D Pitaevskii model
- Global-in-time Well-posedness of the One-dimensional Hydrodynamic Gross-Pitaevskii Equations without Vacuum
- Superfluids Passing an Obstacle and Vortex Nucleation
- Exotic traveling waves for a quasilinear Schrödinger equation with nonzero background