To start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ODE. Then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. It is required to state that the infinite series method is a well-organized method for obtaining exact s...

Computational modeling and the theory of nonlinear dynamical systems allow one to not simply describe the events of the cell cycle, but also to understand why these events occur, just as the theory of gravitation allows one to understand why cannonballs fly in parabolic arcs. The simplest examples of the eukaryotic cell cycle operate like autonomous oscillators. Here, we present the basic theor...

Optical biosensors are often used to measure kinetic rate constants associated with chemical reactions. Such instruments operate in the surface-volume configuration, in which ligand molecules are convected through a fluid-filled volume over a surface to which receptors are confined. Currently, scientists are using optical biosensors to measure the kinetic rate constants associated with DNA tran...

This paper treats a new approach to the problem of periodic signal estimation. The idea is to model the periodic signal as a function of the state of a second order nonlinear ordinary differential equation (ODE). This is motivated by Poincare theory which is useful for proving the existence of periodic orbits for second order ODEs. The functions of the right hand side of the nonlinear ODE are t...

In this paper we study a nonlinear system of differential equations which arises from a stationary 2-dimensional Ice-Sheet Model describing the ice-streaming phenomenon. The system consists of a multivalued nonlinear PDE of parabolic type coupled with a first order PDE and an ODE involving a nonlocal term. We study the uniqueness of weak solution under suitable assumptions (physically reasonabl...

In this article, we propose a generalization of the theory of di usion approximation for random ODE to a nonlinear system of random Schrödinger equations. This system arises in the study of pulse propagation in randomly birefringent optical bers. We rst show existence and uniqueness of solutions for the random PDE and the limiting equation. We follow the work of Garnier-Marty [16, 20], where a ...

In this article, we propose a generalization of the theory of diffusion approximation for random ODE to a nonlinear system of random Schrödinger equations. This system arises in the study of pulse propagation in randomly birefringent optical fibers. We first show existence and uniqueness of solutions for the random PDE and the limiting equation. We follow the work of Garnier-Marty [16, 20], whe...

In this paper we propose a class of second derivative multistep methods for solving some well-known classes of LaneEmden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. These methods, which have good stability and accuracy properties, are useful in deal with stiff ODEs. We show superiority of these methods by applying them on the some famous Lane-...

In this paper, we propose a novel method of blind signal separation using a new performance criterion with nonlinear separating functions, and derive an adaptive algorithm. The criterion consists of nonlinear mappings of output signals and their cumulants for independence of the signals. We show that our method requires a weak condition for stable separation through the ODE analysis. Simulation...

We focused on the analytical analysis of steady flow nanofluid, viscous dissipation with convective boundary condition in this work. The MWCNT and SWCNT are used to described nanofluid. A similarity transformation is applied convert nonlinear PDE from their dimensional form dimensionless ODE. developed ODE for velocity temperature profiles solved by using an approximate technique called homotop...