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...

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...

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...

We introduce an elastic beam Bernoulli–Euler model for the axoneme (cytoskeletal inner core of eukaryotic cells appendages) whose dynamics is controlled by internally generated torques at the inflexion points of the beam. We calculate the geometrical and the mechanical parameters of the...

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...

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...

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...

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...

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...