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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

Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices

Dehghan, Mehdi - In: Mathematics and Computers in Simulation (MATCOM) 71 (2006) 1, pp. 16-30

Several finite difference schemes are discussed for solving the two-dimensional Schrodinger equation with Dirichlet’s boundary conditions. We use three fully implicit finite difference schemes, two fully explicit finite difference techniques, an alternating direction implicit procedure and the...

Persistent link: https://www.econbiz.de/10010749971

Compact and noncompact structures in a class of nonlinearly dispersive equations

Wazwaz, Abdul-Majid; Taha, Thiab - In: Mathematics and Computers in Simulation (MATCOM) 62 (2003) 1, pp. 171-189

. We show that the focusing branches provide compactons solutions: solitons with compact support. We also show that the …

Persistent link: https://www.econbiz.de/10010870291

A numerical study of compactons

Ismail, M.S.; Taha, T.R. - In: Mathematics and Computers in Simulation (MATCOM) 47 (1998) 6, pp. 519-530

The Korteweg–de Vries equation has been generalized by Rosenau and Hyman [Compactons: Solitons with finite wavelength … compactons, they re-emerge with the same coherent shape [Rosenau and Hyman, Compactons: Solitons with finite wave length, Phys …

Persistent link: https://www.econbiz.de/10010870509

Abelian solitons

Donagi, Ron Y.; Previato, Emma - In: Mathematics and Computers in Simulation (MATCOM) 55 (2001) 4, pp. 407-418

solitons. …

Persistent link: https://www.econbiz.de/10010870657

Integrability of a differential-difference KP equation with self-consistent sources

Gegenhasi; Hu, Xing-Biao - In: Mathematics and Computers in Simulation (MATCOM) 74 (2007) 2, pp. 145-158

We introduce a differential-difference KP equation with self-consistent sources (DΔ KPESCS) which is a generalization of the DΔ KP equation. The integrability of the differential-difference equation is shown through bilinear transformation method and Wronskian technique: it possesses N-soliton...

Persistent link: https://www.econbiz.de/10011050453

Averaged models for passive mode-locking using nonlinear mode-coupling

Proctor, J.; Kutz, J. Nathan - In: Mathematics and Computers in Simulation (MATCOM) 74 (2007) 4, pp. 333-342

An averaged mode-locking model is presented in which the nonlinear mode-coupling behavior in a wave-guide array, dual-core fiber, and/or fiber array is used to achieve stable and robust passive mode-locking. By using the discrete, nearest-neighbor spatial coupling of these nonlinear...

Persistent link: https://www.econbiz.de/10011050465

Soliton trains and vortex streets as a form of Cerenkov radiation in trapped Bose–Einstein condensates

Carretero-González, R.; Kevrekidis, P.G.; … - In: Mathematics and Computers in Simulation (MATCOM) 74 (2007) 4, pp. 361-369

We numerically study the nucleation of gray solitons and vortex–antivortex pairs created by a moving impurity in … linear regimes corresponding to small and large velocities. Effectively, the emission of gray solitons and vortex … small density. At longer times, the first nucleation is followed by generation of an array of solitons in 1D (“soliton train …

Persistent link: https://www.econbiz.de/10011050487

On solitons in microstructured solids and granular materials

Salupere, A.; Engelbrecht, J.; Ilison, O.; Ilison, L. - In: Mathematics and Computers in Simulation (MATCOM) 69 (2005) 5, pp. 502-513

The problems under consideration are related to wave propagation in nonlinear dispersive media, characterised by higher-order nonlinear and higher-order dispersive effects. Particularly two problems — wave propagation in dilatant granular materials and wave propagation in shape-memory alloys...

Persistent link: https://www.econbiz.de/10011050562

A study of nonlinear dispersive equations with solitary-wave solutions having compact support

Wazwaz, A.M. - In: Mathematics and Computers in Simulation (MATCOM) 56 (2001) 3, pp. 269-276

, which exhibits compactons—solitons with finite wavelength—is solved exactly. Two numerical illustrations, K(2,2) and K(3 …

Persistent link: https://www.econbiz.de/10011050745