THREE-DIMENSIONAL LIGHT BULLETS IN CUBIC–QUINTIC MEDIA STABILIZED BY PERIODIC VARIATION OF DIFFRACTION AND DISPERSION

2010 ◽  
Vol 19 (03) ◽  
pp. 459-470 ◽  
Author(s):  
P. A. SUBHA ◽  
K. K. ABDULLAH ◽  
V. C. KURIAKOSE
Keyword(s):  
Numerical Methods ◽  
Variational Analysis ◽  
Schrodinger Equation ◽  
Averaging Method ◽  
Three Dimensional ◽  
Periodic Variation ◽  
Varying Coefficients ◽  
Varying Dispersion ◽  
Light Bullets ◽  
Quintic Nonlinear Schrödinger Equation

We propose a dispersion-managed model with diffraction management for the stabilization of three-dimensional spatiotemporal solitons in bulk cubic–quintic media. The cubic–quintic nonlinear Schrödinger equation with periodically varying dispersion and diffraction has been studied using analytical and numerical methods. Variational analysis and the Kapitsa averaging method have been used to study the system analytically. The study has shown that periodically varying coefficients of diffraction and dispersion stabilizes the spatiotemporal solitons in cubic–quintic media.

SPATIOTEMPORAL STRONGLY NONLOCAL SPHERICAL LIGHT BULLETS

2013 ◽  
Vol 22 (01) ◽  
pp. 1350006
Author(s):  
WEI-PING ZHONG
Keyword(s):  
Numerical Simulations ◽  
Legendre Polynomials ◽  
Schrodinger Equation ◽  
Laguerre Polynomials ◽  
Three Dimensional ◽  
Integration Constant ◽  
Generalized Laguerre Polynomials ◽  
Existence And Stability ◽  
Light Bullets ◽  
Nonlocal Nonlinear

The general spherical beam solution of the three-dimensional (3D) spatiotemporal strongly nonlocal nonlinear (NN) Schrödinger equation in the form of light bullets is presented. The 3D spatiotemporal spherical beams are built by the products of generalized Laguerre polynomials and associated Legendre polynomials. By the choice of a specific integration constant, the spherical beam becomes an accessible soliton, which can exist in various forms. We confirm the existence and stability of these solutions by numerical simulations.

Bifurcating bright and dark solitary waves for the perturbed cubic-quintic nonlinear Schrödinger equation

1998 ◽  
Vol 128 (3) ◽  
pp. 585-629 ◽  
Author(s):  
Todd Kapitula
Keyword(s):  
Schrödinger Equation ◽  
Solitary Waves ◽  
Schrodinger Equation ◽  
Three Dimensional ◽  
Small Error ◽  
Heteroclinic Cycle ◽  
Perturbation Techniques ◽  
Ginzburg Landau ◽  
The Waves ◽  
Quintic Nonlinear Schrödinger Equation

The existence of bright and dark multi-bump solitary waves for Ginzburg–Landau type perturbations of the cubic-quintic Schrodinger equation is considered. The waves in question are not perturbations of known analytic solitary waves, but instead arise as a bifurcation from a heteroclinic cycle in a three-dimensional ODE phase space. Using geometric singular perturbation techniques, regions in parameter space for which 1-bump bright and dark solitary waves will bifurcate are identified. The existence of N-bump dark solitary waves (N ≧ 1) is shown via an application of the Exchange Lemma with Exponentially Small Error. N-bump bright solitary waves are shown to exist as a consequence of the work of Kapitula and Maier-Paape.

Optimization of the Navy’s three-dimensional mine impact burial prediction simulation model, Impact35, using high-order numerical methods

2021 ◽  
pp. 154851292110286
Author(s):  
Athanasios Donas ◽  
Ioannis Famelis ◽  
Peter C Chu ◽  
George Galanis
Keyword(s):  
Numerical Analysis ◽  
Numerical Methods ◽  
Prediction Model ◽  
Simulation Model ◽  
Three Dimensional ◽  
Simulation System ◽  
High Order ◽  
Alternative Methodology ◽  
Runge Kutta ◽  
Fifth Order

The aim of this paper is to present an application of high-order numerical analysis methods to a simulation system that models the movement of a cylindrical-shaped object (mine, projectile, etc.) in a marine environment and in general in fluids with important applications in Naval operations. More specifically, an alternative methodology is proposed for the dynamics of the Navy’s three-dimensional mine impact burial prediction model, Impact35/vortex, based on the Dormand–Prince Runge–Kutta fifth-order and the singly diagonally implicit Runge–Kutta fifth-order methods. The main aim is to improve the time efficiency of the system, while keeping the deviation levels of the final results, derived from the standard and the proposed methodology, low.

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