Tricritical point as a crossover between type-Is and type-IIs bifurcations

2023/10/02 by Prabakaran Rajamanickam, Rajamanickam, Prabakaran, Joe͏̈l Daou +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #FOS: Engineering and technology #Geometric Analysis and Curvature Flows #Nonlinear Waves and Solitons

paper · doi:10.13023/psmij.2023.04-01-02

openalex publication_date 2023/10/02 · openalex created_date 2024/07/03 · openalex updated_date 2026/07/28

Abstract

A tricritical point as a crossover between (stationary finite-wavelength) type-I_s and (stationary longwave) type-II_s bifurcations is identified in the study of diffusive-thermal (Turing) instability of flames propagating in a Hele-Shaw channel in a direction transverse to a shear flow. Three regimes exhibiting different scaling laws are identified in the neighbourhood of the tricritical point. For these three regimes, sixth-order partial differential equations are obtained governing the weakly nonlinear evolution of unstable solutions near the onset of instability. These sixth-order PDES may be regarded as the substitute for the classical fourth-order Kuramoto--Sivashinsky equation which is not applicable near the tricritical point.

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