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Traveling-wave solutions for a discrete Burgers equation with nonlinear diffusion

Mickens, Ronald E. - In: Mathematics and Computers in Simulation (MATCOM) 80 (2009) 4, pp. 855-859

We construct a nonstandard finite difference (NSFD) scheme for a Burgers type partial differential equation (PDE) for which the diffusion coefficient has a linear dependence on the dependent variable. After a study of this PDE's traveling-wave solutions, we examine the corresponding properties...

Persistent link: https://www.econbiz.de/10010870582

A numerical comparison of partial solutions in the decomposition method for linear and nonlinear partial differential equations

Kaya, Doǧan; Yokus, Asif - In: Mathematics and Computers in Simulation (MATCOM) 60 (2002) 6, pp. 507-512

In this study, the decomposition method for solving the linear heat equation and nonlinear Burgers equation is implemented with appropriate initial conditions. The application of the method demonstrated that the partial solution in the x-direction requires more computational work when compared...

Persistent link: https://www.econbiz.de/10011051178

A nonstandard finite difference scheme for the diffusionless Burgers equation with logistic reaction

Mickens, Ronald E. - In: Mathematics and Computers in Simulation (MATCOM) 62 (2003) 1, pp. 117-124

A nonstandard finite difference scheme is constructed for the Burgers partial differential equation having no diffusion and a nonlinear logistic reaction term. This scheme preserves the positivity and boundedness properties of the original differential equation and includes the a priori...

Persistent link: https://www.econbiz.de/10010749352

Internally generated nonlinear waves in filament bundles

Ludu, A.; Hutchings, N. - In: Mathematics and Computers in Simulation (MATCOM) 74 (2007) 2, pp. 179-189

We develop a geometrical approach for the relative sliding (shear) between filaments in a bundle subjected to bending and twisting deformations, with applications to motility in flagellated cells. Particular examples for helical and toroidal shapes, and combinations of these, are discussed. The...

Persistent link: https://www.econbiz.de/10010870245

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

Ultracold atoms in 1D optical lattices: mean field, quantum field, computation, and soliton formation

Mishmash, R.V.; Carr, L.D. - In: Mathematics and Computers in Simulation (MATCOM) 80 (2009) 4, pp. 732-740

states. Using a truncated form of these mean-field states as initial conditions, we build quantum analogs to the dark soliton …

Persistent link: https://www.econbiz.de/10011050845

Domain walls of single-component Bose–Einstein condensates in external potentials

Kevrekidis, P.G.; Malomed, B.A.; Frantzeskakis, D.J.; … - In: Mathematics and Computers in Simulation (MATCOM) 69 (2005) 3, pp. 334-345

We demonstrate the possibility of creating domain walls described by a single component Gross–Pitaevskii equation with attractive interactions, in the presence of an optical–lattice potential. While it is found that the domain wall is unstable in an infinite system, we show that the external...

Persistent link: https://www.econbiz.de/10011050961

Dark soliton dynamics in spatially inhomogeneous media: Application to Bose–Einstein condensates

Theocharis, G.; Frantzeskakis, D.J.; Kevrekidis, P.G.; … - In: Mathematics and Computers in Simulation (MATCOM) 69 (2005) 5, pp. 537-552

soliton. Analytical results, based on perturbation techniques, for the motion of the dark soliton are obtained and compared to … may capture and drag a dark soliton. …

Persistent link: https://www.econbiz.de/10011050965