Wave patterns within the generalized convection-reaction-diffusion equation
Vsevolod Vladimirov
TL;DR
This paper investigates wave solutions in a hyperbolic generalization of the convection-reaction-diffusion equation, highlighting the emergence of compactly supported solutions, shock fronts, solitons, and peakons through analytical and numerical methods.
Contribution
It introduces new wave solutions in a hyperbolic convection-reaction-diffusion model using local nonlinear analysis and simulations.
Findings
Identification of compactly supported solutions
Discovery of shock fronts and peakons
Numerical validation of wave behaviors
Abstract
A set of travelling wave solutions to a hyperbolic generalization of the convection-reaction-diffusion is studied by the methods of local nonlinear alnalysis and numerical simulation. Special attention is paid to displaying appearance of the compactly supported soloutions, shock fronts, soliton-like solutions and peakons
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Taxonomy
TopicsNonlinear Waves and Solitons · Nonlinear Photonic Systems · Differential Equations and Numerical Methods