10 citations · 56 across the 11 of their papers we have counts for
11 papers
A Finite Difference Scheme for (2+1)D Cubic-Quintic Nonlinear Schrödinger Equations with Nonlinear Damping
Anh Ha Le, Toan T. Huynh, Quan M. Nguyen
Solitons of the purely cubic nonlinear Schrödinger equation in a space dimension of suffer critical and supercritical collapses. These solitons can be stabilized in a cu…
Highly controllable stabilization and switching of multiple colliding soliton sequences with generic Ginzburg-Landau gain-loss
Avner Peleg, Toan T. Huynh
We investigate propagation of J soliton sequences in a nonlinear optical waveguide array with generic weak Ginzburg-Landau (GL) gain-loss and nearest-neighbor (NN) interaction. The…
Analysis of a Crank-Nicolson finite difference scheme for (2+1)D perturbed nonlinear Schrödinger equations with saturable nonlinearity
Anh-Ha Le, Toan T. Huynh, Quan M. Nguyen
We analyze a Crank-Nicolson finite difference discretization for the perturbed (2+1)D nonlinear Schrödinger equation with saturable nonlinearity and a perturbation of cubic loss. W…
Fast two-pulse collisions in linear diffusion-advection systems with weak quadratic loss in spatial dimension 2
Avner Peleg, Toan T. Huynh
We investigate the dynamics of fast two-pulse collisions in linear diffusion-advection systems with weak quadratic loss in spatial dimension 2. We introduce a two-dimensional pertu…
Strong effects of fast collisions between pulsed optical beams in a linear medium with weak cubic loss
Avner Peleg, Toan T. Huynh
We investigate fast collisions between pulsed optical beams in a linear medium with weak cubic loss that arises due to nondegenerate two-photon absorption. We introduce a perturbat…
Fast two-beam collisions in a linear optical medium with weak cubic loss in spatial dimension higher than 1
Avner Peleg, Toan T. Huynh, Quan M. Nguyen
We study the dynamics of fast two-beam collisions in linear optical media with weak cubic loss in spatial dimension higher than 1. For this purpose, we extend the perturbation theo…
Collision-induced amplitude dynamics of fast 2D solitons in saturable nonlinear media with weak nonlinear loss
Quan M. Nguyen, Toan T. Huynh
We study the amplitude dynamics of two-dimensional (2D) solitons in a fast collision described by the coupled nonlinear Schrödinger equations with a saturable nonlinearity and weak…
Universality of the amplitude shift in fast two-pulse collisions in weakly perturbed linear physical systems
Quan M. Nguyen, Toan T. Huynh, Avner Peleg
We demonstrate that the amplitude shifts in fast two-pulse collisions in perturbed linear physical systems with weak nonlinear dissipation exhibit universal soliton-like behavior.…
Frequency shifting for solitons based on transformations on the Fourier domain and applications
Quan M. Nguyen, Toan T. Huynh
We develop the theoretical procedures for shifting the frequency of a single soliton and of a sequence of solitons of the nonlinear Schrödinger equation. The procedures are based o…
Soliton-like behavior in fast two-pulse collisions in weakly perturbed linear physical systems
Avner Peleg, Quan M. Nguyen, Toan T. Huynh
We demonstrate that pulses of linear physical systems, weakly perturbed by nonlinear dissipation, exhibit soliton-like behavior in fast collisions. The behavior is demonstrated for…
Stable scalable control of soliton propagation in broadband nonlinear optical waveguides
Avner Peleg, Quan M. Nguyen, Toan T. Huynh
We develop a method for achieving scalable transmission stabilization and switching of colliding soliton sequences in optical waveguides with broadband delayed Raman response a…