A family of travelling wave solutions to the Fisher-KPP equation with speeds $c=\pm 5/\sqrt{6}$ can be expressed exactly using Weierstrass elliptic functions. The well-known solution for $c=5/\sqrt{6}$, which decays zero in far-field, is exceptional sense that it written simply terms an exponential function. This has property phase-plane trajectory a heteroclinic orbit beginning at saddle point...

In this paper we study numerical methods for solving integro-differential equations which generalize the well-known Fisher equation. The numerical methods are obtained considering the MOL (Method of Lines) approach. The stability and convergence of the methods are studied. Numerical results illustrating the theoretical results proved are also included. © 2006 IMACS. Published by Elsevier B.V. A...

We investigate the singular limit, as ε → 0, of the Fisher equation ∂tu = ε∆u+ ε u(1− u) in the whole space. We consider initial data with compact support plus, possibly, perturbations very small as ‖x‖ → ∞. By proving both generation and motion of interface properties, we show that the sharp interface limit moves by a constant speed, which is the minimal speed of some related one-dimensional t...

A generalized Fisher equation (GFE) relates the time derivative of the average of the intrinsic rate of growth to its variance. The GFE is an exact mathematical result that has been widely used in population dynamics and genetics, where it originated. Here we demonstrate that the GFE can also be useful in other fields, specifically in chemistry, with models of two chemical reaction systems for ...

Lie symmetry group method is applied to study the Fisher-Kolmogorov equation. The symmetry group is given, and travelling wave solutions are obtained. Finally the conservation laws are determined.

The Fisher information can be used to indicate the precision of parameter estimation by the quantum Cramér-Rao inequality. This paper presents an efficient numerical algorithm for the calculation of Fisher information based on quantum weak measurement. According to the quantum stochastic master equation, the Fisher information is expressed in the form of log-likelihood functions. Three main met...

We investigate the detailed connection between the Wright-Fisher model of random genetic drift and the diffusion approximation, under the assumption that selection and drift are weak and so cause small changes over a single generation. A representation of the mathematics underlying the Wright-Fisher model is introduced which allows the connection to be made with the corresponding mathematics un...

We present two extended forms of Fisher information that fit well in the context of nonextensive thermostatistics. We show that there exists an interplay between these generalized Fisher information, the generalized q-Gaussian distributions and the q-entropies. The minimum of the generalized Fisher information among distributions with a fixed moment, or with a fixed qentropy is attained, in bot...

The modified simple equation method is employed to find the exact traveling wave solutions involving parameters for nonlinear evolution equations namely, a diffusive predator-prey system, the Bogoyavlenskii equation, the generalized Fisher equation and the Burgers-Huxley equation. When these parameters are taken special values, the solitary wave solutions are derived from the exact traveling wa...