Reductions and exact solutions of Lotka–Volterra and more complex reaction–diffusion systems with delays

2021 ◽  
pp. 107731
Author(s):  
Andrei D. Polyanin ◽  
Vsevolod G. Sorokin
Keyword(s):  
Exact Solutions ◽  
Reaction Diffusion ◽  
Complex Reaction ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems

scholarly journals A reaction–diffusion system with cross-diffusion: Lie symmetry, exact solutions and their applications in the pandemic modelling

2021 ◽  
pp. 1-18
Author(s):  
ROMAN M. CHERNIHA ◽  
VASYL V. DAVYDOVYCH
Keyword(s):  
Exact Solutions ◽  
Reaction Diffusion ◽  
Interesting Case ◽  
Lie Symmetry ◽  
Point Of View ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Reaction Diffusion Systems ◽  
Cross Diffusion ◽  
Diffusion Systems

A non-linear reaction–diffusion system with cross-diffusion describing the COVID-19 outbreak is studied using the Lie symmetry method. A complete Lie symmetry classification is derived and it is shown that the system with correctly specified parameters admits highly non-trivial Lie symmetry operators, which do not occur for all known reaction–diffusion systems. The symmetries obtained are also applied for finding exact solutions of the system in the most interesting case from applicability point of view. It is shown that the exact solutions derived possess typical properties for describing the pandemic spread under 1D approximation in space and lead to the distributions, which qualitatively correspond to the measured data of the COVID-19 spread in Ukraine.

scholarly journals Exact Solutions of Low-Dimensional Reaction-Diffusion Systems

1997 ◽  
Vol 11 (01n02) ◽  
pp. 109-114 ◽  
Author(s):  
António M. R. Cadilhe ◽  
M. Lawrence Glasser ◽  
Vladimir Privman
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Reaction Diffusion ◽  
Single Species ◽  
Exact Results ◽  
Reaction Diffusion Systems ◽  
Diffusion Limited ◽  
Diffusion Systems ◽  
Novel Method ◽  
Low Dimensional

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 like particles, obtained by a novel method which allows exact solution of certain single-species and two-species reactions, are discussed.

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