A numerical study of the semi-classical limit of the focusing nonlinear Schrödinger equation
From MaRDI portal
Publication:1850720
DOI10.1016/S0375-9601(01)00011-1zbMath1005.81029OpenAlexW2141910262MaRDI QIDQ1850720
Hector D. Ceniceros, Fei-Ran Tian
Publication date: 18 December 2002
Published in: Physics Letters. A (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0375-9601(01)00011-1
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)
Related Items
On universality of critical behavior in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the Tritronquée solution to the Painlevé-I equation ⋮ The Gaussian semiclassical soliton ensemble and numerical methods for the focusing nonlinear Schrödinger equation ⋮ High-order conservative schemes for the nonlinear Schrödinger equation in the semiclassical limit ⋮ Discrete conservation laws and the convergence of long time simulations of the mKdV equation ⋮ Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert problem approach ⋮ Large time-stepping spectral methods for the semiclassical limit of the defocusing nonlinear Schrödinger equation ⋮ Numerical simulation of a generalized Zakharov system ⋮ A second look at the Gaussian semiclassical soliton ensemble for the focusing nonlinear Schrödinger equation ⋮ On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation ⋮ Compact Exponential Conservative Approaches for the Schrödinger Equation in the Semiclassical Regimes ⋮ On critical behaviour in systems of Hamiltonian partial differential equations
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Semiclassical eigenvalue distribution of the Zakharov-Shabat eigenvalue problem
- Removing the stiffness from interfacial flows with surface tension
- Onset of oscillations in nonsoliton pulses in nonlinear dispersive fibers
- On the semiclassical limit of the focusing nonlinear Schrödinger equation
- Dispersive approximations in fluid dynamics
- Singular Solutions and Ill-Posedness for the Evolution of Vortex Sheets
- A study of singularity formation in a vortex sheet by the point-vortex approximation
- The Zero Dispersion Limit of the Korteweg-de Vries Equation With Periodic Initial Data
- On dispersive difference schemes. I
- Multiphase averaging and the inverse spectral solution of the Korteweg—de Vries equation
- The semiclassical limit of the defocusing NLS hierarchy
- [https://portal.mardi4nfdi.de/wiki/Publication:4257037 On the Whitham equations for the semiclassical limit of the defocusing nonlinear Schr�dinger equation]
- A continuum limit of the Toda lattice
- A soliton on a vortex filament