Ronald M. Caplan

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a r t i c l e i n f o a b s t r a c t Linearized numerical stability bounds for solving the nonlinear time-dependent Schrödinger equation (NLSE) using explicit finite-differencing are shown. The bounds are computed for the fourth-order Runge–Kutta scheme in time and both second-order and fourth-order central differencing in space. Results are given for(More)
We present a simple to use, yet powerful code package called NLSEmagic to numerically integrate the nonlinear Schrödinger equation in one, two, and three dimensions. NLSEmagic is a high-order finite-difference code package which utilizes graphic processing unit (GPU) parallel architectures. The codes running on the GPU are many times faster than their(More)
We revisit the topic of the existence and azimuthal modulational stability of solitary vortices (alias vortex solitons) in the two-dimensional (2D) cubic–quintic nonlinear Schrödinger equation. We develop a semi-analytical approach, assuming that the vortex soliton is relatively narrow, which allows one to effectively split the full 2D equation into radial(More)
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