Computer algebra, Painlevé analysis and the time-dependent-coefficient nonlinear Schrödinger equation
نویسندگان
چکیده
منابع مشابه
Uniform semiclassical approximations of the nonlinear Schrödinger equation by a Painlevé mapping
A useful semiclassical method to calculate eigenfunctions of the Schrödinger equation is the mapping to a well-known ordinary differential equation, as for example Airy’s equation. In this paper we generalize the mapping procedure to the nonlinear Schrödinger equation or Gross-Pitaevskii equation describing the macroscopic wave function of a Bose-Einstein condensate. The nonlinear Schrödinger e...
متن کاملMultiresolution scheme for Time-Dependent Schrödinger Equation
Article history: Received 3 November 2009 Accepted 21 November 2009 Available online xxxx
متن کاملAn exponential time differencing method for the nonlinear Schrödinger equation
The spectral methods offer very high spatial resolution for a wide range of nonlinear wave equations, so, for the best computational efficiency, it should be desirable to use also high order methods in time but without very strict restrictions on the step size by reason of numerical stability. In this paper we study the exponential time differencing fourth-order Runge-Kutta (ETDRK4) method; thi...
متن کاملSemi-global approach for propagation of the time-dependent Schrödinger equation for time-dependent and nonlinear problems
A detailed exposition of highly efficient and accurate method for the propagation of the time-dependent Schrödinger equation [50] is presented. The method is readily generalized to solve an arbitrary set of ODE’s. The propagation is based on a global approach, in which large time-intervals are treated as a whole, replacing the local considerations of the common propagators. The new method is su...
متن کاملMathematical modeling : control of the Time Dependent Schrödinger Equation
81Q05 Synonyms or related entries control of quantum dynamics by electromagnetic radiation; laser control of chemical reactions; control of spin systems; control in Nuclear Magnetic Resonance; construction of logic gates for quantum computers Definition Quantum control is the control, at the quantum level, of the state or dynamical evolution of some quantum system by means of electromagnetic ra...
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: Computers & Mathematics with Applications
سال: 1996
ISSN: 0898-1221
DOI: 10.1016/0898-1221(96)00068-5