As an application of Hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. We have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear Backlund transformations and construction of ...

Models that deal with the individual level of populations have shown the importance of stochasticity in ecology, epidemiology and evolution. An increasingly common approach to studying these models is through stochastic (event-driven) simulation. One striking disadvantage of this approach is the need for a large number of replicates to determine the range of expected behaviour. Here, for a clas...

In this paper we use a stochastic differential equation to describe the dynamic evolution of the height of an individual tree. The first model is defined by Gompertz shape stochastic differential equation. The second model is defined by Gompertz stochastic differential equation with a threshold parameter. This model can be considered as an extension of the three parameter stochastic Gompertz mo...

This paper studies finite element approximations of the stochastic Allen–Cahn equation with gradient-type multiplicative noise that is white in time and correlated in space. The sharp interface limit—as the diffuse interface thickness vanishes—of the stochastic Allen–Cahn equation is formally a stochastic mean curvature flow which is described by a stochastically perturbed geometric law of the ...

We compute statistical properties of the stochastic entropy production associated with the nonstationary transport of heat through a system coupled to a time dependent nonisothermal heat bath. We study the one-dimensional stochastic evolution of a bound particle in such an environment by solving the appropriate Langevin equation numerically, and by using an approximate analytic solution to the ...

The effects of stochastic perturbations in a nonlinear alpha Omega-dynamo model are investigated. By using transformation of variables we identify a "slow" variable that determines the global evolution of the non-normal alpha Omega-dynamo system in the subcritical case. We apply an adiabatic elimination procedure to derive a closed stochastic differential equation for the slow variable for whic...

We consider a stochastic susceptible-exposed-infected-recovered (SEIR) epidemiological model. Through the use of a normal form coordinate transform, we are able to analytically derive the stochastic center manifold along with the associated, reduced set of stochastic evolution equations. The transformation correctly projects both the dynamics and the noise onto the center manifold. Therefore, t...