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A linearly implicit conservative scheme for the coupled nonlinear Schrödinger equation

Ismail, M.S.; Taha, Thiab R. - In: Mathematics and Computers in Simulation (MATCOM) 74 (2007) 4, pp. 302-311

The coupled nonlinear Schrödinger equation models several intersting physical phenomena. It presents a model equation for optical fiber with linear birefringence. In this paper, we present a linearly implicit conservative method to solve this equation. This method is second order accurate in...

Persistent link: https://www.econbiz.de/10011051245

Asymptotic solutions for a multi-anticipative car-following model

Wagner, Christoph - In: Physica A: Statistical Mechanics and its Applications 260 (1998) 1, pp. 218-224

Using a long wave expansion we study the asymptotic solutions near a critical point of a multi-anticipative car-following model. A suitable rescaling of the variables then yields a modified Korteweg–de Vries (MKdV) equation with higher order corrections. An equation of this general form has...

Persistent link: https://www.econbiz.de/10010873049

Analytic solutions for nonlinear waves in coupled reacting systems

Abramson, G.; Kenkre, V.M.; Bishop, A.R. - In: Physica A: Statistical Mechanics and its Applications 305 (2002) 3, pp. 427-436

We analyze a system of reacting elements harmonically coupled to nearest neighbors in the continuum limit. An analytic solution is found for traveling waves. The procedure is used to find oscillatory as well as solitary waves. A comparison is made between exact solutions and solutions of the...

Persistent link: https://www.econbiz.de/10010874184

Multidimensional aspects of nonlinear electromagnetic solitary pulses

Bonatto, A.; Nunes, R.P.; Bonatto, C.; Pakter, R.; … - In: Physica A: Statistical Mechanics and its Applications 404 (2014) C, pp. 332-340

excitations of space-charge modes are analyzed and the endurance of trains of solitons against transverse effects is clarified. …

Persistent link: https://www.econbiz.de/10010931522

Numerical simulation of two-dimensional sine-Gordon solitons via a split cosine scheme

Sheng, Q.; Khaliq, A.Q. M.; Voss, D.A. - In: Mathematics and Computers in Simulation (MATCOM) 68 (2005) 4, pp. 355-373

numerical stability. Numerical demonstrations for colliding circular solitons are given. …

Persistent link: https://www.econbiz.de/10010749626

Propagation of sech2-type solitary waves in hierarchical KdV-type systems

Ilison, Lauri; Salupere, Andrus - In: Mathematics and Computers in Simulation (MATCOM) 79 (2009) 11, pp. 3314-3327

A hierarchical Korteweg–de Vries-type evolution equation is applied for modelling wave propagation in dilatant granular materials. The model equation is integrated numerically under sech2-type initial conditions using the Fourier transform-based pseudospectral method. Numerical simulations are...

Persistent link: https://www.econbiz.de/10010749632

Nonlinear dispersion relations

Ludu, A.; Kevrekidis, P.G. - In: Mathematics and Computers in Simulation (MATCOM) 74 (2007) 2, pp. 229-236

We examine how nonlinear dispersion relations (NLDR) can be used as a simple, universal algebraic tool to provide information for the localized, nonlinear solutions of PDE that model physical systems. Such scaling relations between width, amplitude and velocity are of great help for numerical...

Persistent link: https://www.econbiz.de/10010749768

Analysis of coupled oceanographic and acoustic soliton simulations in the Yellow Sea: a search for soliton-induced resonances

Chin-Bing, S.A.; Warn-Varnas, A.; King, D.B.; Lamb, K.G.; … - In: Mathematics and Computers in Simulation (MATCOM) 62 (2003) 1, pp. 11-20

by solitary internal waves (solitons). Their hypothesis remains unsubstantiated due to a scarcity of oceanographic … measurements in this area. In this simulation study the non-hydrostatic, 2.5-dimensional Lamb model was used to generate solitons … lead to the formulation of internal bores and solitons. SAR observations of solitons near this region were used to select …

Persistent link: https://www.econbiz.de/10010750028

Two-scale numerical solution of the electromagnetic two-fluid plasma-Maxwell equations: Shock and soliton simulation

Baboolal, S.; Bharuthram, R. - In: Mathematics and Computers in Simulation (MATCOM) 76 (2007) 1, pp. 3-7

–463]. Allowing for wave propagation in one dimension, we illustrate the formation and evolution of magnetosonic shocks and solitons …

Persistent link: https://www.econbiz.de/10010750051

On the propagation of 1D solitary waves in Mindlin-type microstructured solids

Tamm, Kert; Salupere, Andrus - In: Mathematics and Computers in Simulation (MATCOM) 82 (2012) 7, pp. 1308-1320

The Mindlin model and hierarchical approach by Engelbrecht and Pastrone are used for modelling 1D wave propagation in microstructured solids. After introducing the free energy function, one gets from Euler–Lagrange equations a system of equations of motion. Making use of the slaving principle,...

Persistent link: https://www.econbiz.de/10010751772