1,814 research outputs found
Compressive Split-Step Fourier Method
In this paper an approach for decreasing the computational effort required
for the split-step Fourier method (SSFM) is introduced. It is shown that using
the sparsity property of the simulated signals, the compressive sampling
algorithm can be used as a very efficient tool for the split-step spectral
simulations of various phenomena which can be modeled by using differential
equations. The proposed method depends on the idea of using a smaller number of
spectral components compared to the classical split-step Fourier method with a
high number of components. After performing the time integration with a smaller
number of spectral components and using the compressive sampling technique with
l1 minimization, it is shown that the sparse signal can be reconstructed with a
significantly better efficiency compared to the classical split-step Fourier
method. Proposed method can be named as compressive split-step Fourier method
(CSSFM). For testing of the proposed method the Nonlinear Schrodinger Equation
and its one-soliton and two-soliton solutions are considered
Self-Localized Solutions of the Kundu-Eckhaus Equation in Nonlinear Waveguides
In this paper we numerically analyze the 1D self-localized solutions of the
Kundu-Eckhaus equation (KEE) in nonlinear waveguides using the spectral
renormalization method (SRM) and compare our findings with those solutions of
the nonlinear Schrodinger equation (NLSE). We show that single, dual and
N-soliton solutions exist for the case with zero optical potentials, i.e. V=0.
We also show that these soliton solutions do not exist, at least for a range of
parameters, for the photorefractive lattices with optical potentials in the
form of V=Io cos^2(x) for cubic nonlinearity. However, self-stable solutions of
the KEE with saturable nonlinearity do exist for some range of parameters. We
compare our findings for the KEE with those of the NLSE and discuss our
results.Comment: Typos are corrected, 8 figures are adde
Early Detection of Rogue Waves by the Wavelet Transforms
We discuss the possible advantages of using the wavelet transform over the
Fourier transform for the early detection of rogue waves. We show that the
triangular wavelet spectra of the rogue waves can be detected at early stages
of the development of rogue waves in a chaotic wave field. Compared to the
Fourier spectra, the wavelet spectra is capable of detecting not only the
emergence of a rogue wave but also its possible spatial (or temporal) location.
Due to this fact, wavelet transform is also capable of predicting the
characteristic distances between successive rogue waves. Therefore multiple
simultaneous breaking of the successive rogue waves on ships or on the offshore
structures can be predicted and avoided by smart designs and operations
Rogue Quantum Harmonic Oscillations
We show the existence and investigate the dynamics and statistics of rogue
oscillations (standing waves) generated in the frame of the nonlinear quantum
harmonic oscillator (NQHO). With this motivation, in this paper, we develop a
split-step Fourier scheme for the computational analysis of NQHO. We show that
modulation instability excites the generation of rogue oscillations in the
frame of the NQHO. We also discuss the effects of various parameters such as
the strength of trapping well potential, nonlinearity, dissipation, fundamental
wave number and perturbation amplitude on rogue oscillation formation
probabilities
Energy spectrum for two-dimensional potentials in very high magnetic fields
A method, analogous to supersymmetry transformation in quantum mechanics, is
developed for a particle in the lowest Landau level moving in an arbitrary
potential. The method is applied to two-dimensional potentials formed by Dirac
delta scattering centers. In the periodic case, the problem is solved exactly
for rational values of the magnetic flux (in units of flux quantum) per unit
cell. The spectrum is found to be self-similar, resembling the Hofstadter
butterfly.Comment: 9 pages, 3 figures, REVTEX, to appear in Phys. Rev. B, Sep. 1
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