Soliton solutions of (2+1)-dimensional non-linear reaction-diffusion model via Riccati-Bernoulli approach

Exact solutions of linear reaction-diffusion processes

8 Many processes during embryonic development involve transport and reaction of molecules, 9 or transport and proliferation of cells, within growing tissues. Mathematical models of 10 such processes usually take the form of a reaction–diffusion partial differential equation 11 (PDE) on a growing domain. Previous analyses of such models have mainly involved solv12 ing the PDEs numerically. Here,...

Soliton-like Solutions of the Complex Non-linear Klein-Gordon Systems in 1 + 1 Dimensions

In this paper, we present soliton-like solutions of the non-linear complex Klein-Gordon systems in 1+1 dimensions. We will use polar representation to introduce three different soliton-like solutions including, complex kinks (anti-kinks), radiative profiles, and localized wave-packets. Complex kinks (anti-kinks) are topological objects with zero electrical charges. Radiative profiles are object...

Travelling Wave Solutions of the One Dimensional Diffusion-reaction Equation

Exact Solutions of Low - Dimensional Reaction - Diffusion Systems

We briefly review some common diffusion-limited reactions with emphasis on results for two-species reactions with anisotropic hopping. Our review also covers single-species reactions. The scope is that of providing reference and general discussion rather than details of methods and results. Recent exact results for a two-species model with anisotropic hopping and with ‘sticky’ interaction of li...

on the effect of linear & non-linear texts on students comprehension and recalling

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