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A third order numerical scheme for the two-dimensional sine-Gordon equation

Bratsos, A.G. - In: Mathematics and Computers in Simulation (MATCOM) 76 (2007) 4, pp. 271-282

A rational approximant of third order, which is applied to a three-time level recurrence relation, is used to transform the two-dimensional sine-Gordon (SG) equation into a second-order initial-value problem. The resulting nonlinear finite-difference scheme, which is analyzed for stability, is...

Persistent link: https://www.econbiz.de/10010748680

Transmission of nonlinear localized modes through waveguide bends

Agrotis, Maria; Kevrekidis, Panayotis G.; Malomed, Boris A. - In: Mathematics and Computers in Simulation (MATCOM) 69 (2005) 3, pp. 223-234

In a recent work, a model for a bend of a nonlinear waveguide in planar geometry was introduced [Yu.S. Kivshar, P.G. Kevrekidis, S. Takeno, Phys. Lett. 307 (2003) 287]. Motivated by photonic-crystal waveguides, we examine transmission of localized pulses through the bend, and identify outcomes...

Persistent link: https://www.econbiz.de/10010749340

Interaction of spatial solitons with a localized spatially-modulated medium

Ramos, J.I - In: Mathematics and Computers in Simulation (MATCOM) 56 (2001) 6, pp. 571-583

increase in frequency may result in a soliton that propagates in the opposite direction to the one encountering the nonuniform … modulation results in a surface wave and a soliton that may propagate towards either the right or left boundary. In either case …

Persistent link: https://www.econbiz.de/10010749357

A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions

Dehghan, Mehdi; Shokri, Ali - In: Mathematics and Computers in Simulation (MATCOM) 79 (2008) 3, pp. 700-715

The nonlinear sine-Gordon equation arises in various problems in science and engineering. In this paper, we propose a numerical scheme to solve the two-dimensional damped/undamped sine-Gordon equation. The proposed scheme is based on using collocation points and approximating the solution...

Persistent link: https://www.econbiz.de/10010749551

Ion-acoustic soliton energy in a plasma with nonextensive electrons

Ait Gougam, Leila; Tribeche, Mouloud - In: Physica A: Statistical Mechanics and its Applications 407 (2014) C, pp. 226-230

of the soliton amplitude and width. The soliton energy is depleted as q increases. …

Persistent link: https://www.econbiz.de/10010777048

Some methods for generating solutions to the Korteweg–de Vries equation

Bracken, Paul - In: Physica A: Statistical Mechanics and its Applications 335 (2004) 1, pp. 70-78

The constraint equation which must hold for the reciprocal of a known solution for the Korteweg–de Vries (KdV) equation to be a solution itself is derived. These reciprocal solutions are required to satisfy a differential equation which is in fact a Painlevé equation. A differential...

Persistent link: https://www.econbiz.de/10010588503

Exact cross kink-wave solutions and resonance for the Jimbo–Miwa equation

Dai, Zhengde; Li, Zitian; Liu, Zhenjiang; Li, Donglong - In: Physica A: Statistical Mechanics and its Applications 384 (2007) 2, pp. 285-290

–Miwa equation by using two-soliton method, bilinear method and transforming parameters into complex ones. Moreover, we investigate …

Persistent link: https://www.econbiz.de/10010588611

Energy transfer in a dispersion-managed Korteweg-de Vries system

Triki, Houria - In: Mathematics and Computers in Simulation (MATCOM) 76 (2007) 4, pp. 283-292

We consider the propagation of weakly nonlinear, weakly dispersive waves in an inhomogeneous media within the framework of the variable-coefficient Korteweg-de Vries equation. An analytical formula with which to compute the energy transfer between neighboring solitary waves is derived. The...

Persistent link: https://www.econbiz.de/10011050250

Positive- and negative-mass solitons in Bose–Einstein condensates with optical lattices

Sakaguchi, H.; Malomed, B.A. - In: Mathematics and Computers in Simulation (MATCOM) 69 (2005) 5, pp. 492-501

analytically that, in the case of the repulsive BEC, where the soliton is of the gap type, its effective mass is negative. In … accordance with this, we demonstrate that such a soliton cannot be held by the usual parabolic trap, but it can be captured … (performing harmonic oscillations) by an anti-trapping inverted parabolic potential. We also study the motion of the soliton in a …

Persistent link: https://www.econbiz.de/10011050596

Numerical solution to coupled nonlinear Schrödinger equations on unbounded domains

Zhou, Shenggao; Cheng, Xiaoliang - In: Mathematics and Computers in Simulation (MATCOM) 80 (2010) 12, pp. 2362-2373

The numerical simulation of coupled nonlinear Schrödinger equations on unbounded domains is considered in this paper. By using the operator splitting technique, the original problem is decomposed into linear and nonlinear subproblems in a small time step. The linear subproblem turns out to be...

Persistent link: https://www.econbiz.de/10011050642