Two-dimensional nonlinear Schrödinger equations and their properties
نویسندگان
چکیده
منابع مشابه
Of Nonlinear Schrödinger Equations
The authors suggest a new powerful tool for solving group classification problems, that is applied to obtaining the complete group classification in the class of nonlinear Schrödinger equations of the form iψt +∆ψ + F (ψ,ψ ∗) = 0.
متن کاملArtificial boundary conditions for one-dimensional cubic nonlinear Schrödinger equations
This paper addresses the construction of nonlinear integro-differential artificial boundary conditions for one-dimensional nonlinear cubic Schrödinger equations. Several ways of designing such conditions are provided and a theoretical classification of their accuracy is given. Semi-discrete time schemes based on the method developed by Durán and Sanz-Serna [IMA J. Numer. Anal. 20 (2) (2000), pp...
متن کاملA spatial sixth-order alternating direction implicit method for two-dimensional cubic nonlinear Schrödinger equations
Based on the combined compact difference scheme, an alternating direction implicit method is proposed for solving two-dimensional cubic nonlinear Schrödinger equations. The proposed method is sixth-order accurate in space and second-order accurate in time. The linear Fourier analysis method is exploited to study the stability of the proposed method. The efficiency and accuracy of the proposed m...
متن کاملUnified approach to split absorbing boundary conditions for nonlinear Schrödinger equations: Two-dimensional case.
This paper aims to design local absorbing boundary conditions (LABCs) for the two-dimensional nonlinear Schrödinger equations on a rectangle by extending the unified approach. Based on the time-splitting idea, the main process of the unified approach is to approximate the kinetic energy part by a one-way equation, unite it with the potential energy equation, and then obtain the well-posed and a...
متن کاملTwo-dimensional supersonic nonlinear Schrödinger flow past an extended obstacle.
Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional (2D) defocusing nonlinear Schrödinger (NLS) equation. This problem is of fundamental importance as a dispersive analog of the corresponding classical gas-dynamics problem. Assuming the oncoming flow speed is sufficiently high, we asymptotically reduce the original ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physica D: Nonlinear Phenomena
سال: 1994
ISSN: 0167-2789
DOI: 10.1016/0167-2789(94)00097-2