Recurrence in Semidiscrete Approximations of the Nonlinear Schrödinger Equation
Copyright policy )Recurrence in Semidiscrete Approximations of the Nonlinear Schrödinger Equation
The use of numerical methods is investigated for a study of recurrence in the nonlinear Schrödinger equation. A spectral, a pseudospectral and a finite difference method are shown to conserve discrete analogues of two of the conservation laws satisfied by this equation. The first and the second method are shown to possess the exact Benjamin-Feir instability limit while the finite difference method has a larger region of instability. The pseudospectral method suffers from some aliasing errors which tend to decrease the recurrence time as well as the side-band amplitudes. A numerical study demonstrates the different behaviour of the methods on a sample problem.
- University of the Free State South Africa
recurrence, Partial differential equations of mathematical physics and other areas of application, pseudospectral method, spectral method, Stability and convergence of numerical methods for boundary value problems involving PDEs, numerical example, Applications to the sciences, region of instability, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, Benjamin-Feir instability, aliasing errors, nonlinear Schrödinger equation, finite difference method
recurrence, Partial differential equations of mathematical physics and other areas of application, pseudospectral method, spectral method, Stability and convergence of numerical methods for boundary value problems involving PDEs, numerical example, Applications to the sciences, region of instability, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, Benjamin-Feir instability, aliasing errors, nonlinear Schrödinger equation, finite difference method
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