This report is devoted to the study and to the comparison of methods for estimation of the local error and for adaptive step-size control when solving the generalised nonlinear Schrodinger equation (GNLSE) in optics by the Interaction Picture (IP) method or by the Symmetric Split-Step (S3F) method. Namely, we propose and study the use of an embedded Runge-Kutta method to solve the nonlinear pro...

Continuouslyphase-locked (autoresonant) dark solitons of the defocusing nonlinear Schrodinger equation are excited and controlled by driving the system by a slowly chirped wavelike perturbation. The theory of these excitations is developed using Whitham's averaged variational principle and compared with numerical simulations. The problem of the threshold for transition to autoresonance in the d...

The ordinary nonlinear Schrodinger equation for deep-water waves (found by a perturbation analysis to 0(€3 ) in the wave steepness €) compares unfavourably with the exact calculations of Longuet-Higgins (1978) for € > 0·10. Dysthe (1979) showed that a significant improvement is found by taking the perturbation analysis one step further to 0(€ ). One of the dominant new effects is the wave-induc...

The electron states in axially symmetric quantum wires are computed by means of the effective mass Schrodinger equation, which is written in cylindrical coordinates \phi, \rho, and z. We show that a direct discretization of the Schrodinger equation by central finite differences leads to a nonsymmetricHamiltonian matrix. Because diagonalization of such matrices is more complex it is advantageous...

The nonlinear Schrodinger (NLS) equation in a self-defocusing Kerr medium supports dark solitons. Moreover the mean field description of a dilute Bose-Einstein condensate (BEC) is described by the Gross-Pitaevskii equation, which for a highly anisotropic (cigar-shaped) magnetic trap reduces to a one-dimensional (1D) cubic NLS in an external potential. A quantum lattice algorithm is developed fo...

The harmonic oscillator in anti de Sitter space(AdS) is discussed. We consider the harmonic oscillator potential and then time independent Schrodinger equation in AdS space. Then we apply the supersymmetric Quantum Mechanics approach to solve our differential equation. In this paper we have solved Schrodinger equation for harmonic oscillator in AdS spacetime by supersymmetry approach. The shape...