On Nonlinear Waves in the Spatio-Temporal Dynamics of Interacting Populations

TL;DR

This paper models the complex spatial-temporal behavior of interacting populations using nonlinear PDEs, deriving analytical solutions that reveal nonlinear wave phenomena like kinks and solitary waves.

Contribution

It introduces a tractable nonlinear PDE model for population dynamics and applies a modified method to find analytical wave solutions.

Findings

Analytical solutions for nonlinear waves in population models.

Identification of kink and solitary wave solutions.

Enhanced understanding of wave phenomena in ecological systems.

Abstract

In this paper the spatial-temporal dynamics of the members of interacting populations is described by nonlinear partial differential equations. We consider the migration as a diffusion process influenced by the changing values of the birth rates and coefficients of interaction between the populations. For the particular case of one population and one spatial dimension the general model is reduced to analytically tractable PDE with polynomial nonlinearity up to third order. By applying the modified method of simplest equation to the described model we obtain an analytical solution which describes nonlinear kink and solitary waves in the population dynamics.