Breather, lump and other symmetric waves-based biological bacterial colonies modeling with generalized Chavy-Waddy-Kolokolnikov analytical solutions

Abstract

This work investigates wave symmetry in bacterial pattern formation for the generalized Chavy-Waddy-Kolokolnikov (CWK) model, a nonlinear framework based on partial differential equations (PDEs). In microbiology, investigating how bacterial colonies develop spatial structures is crucial to analyzing their adaptive behaviors. By employing the Hirota bilinear transformation, we constructed numerous symmetric wave structures such as solitons, homoclinic breathers, periodic cross-kink, lumps, and M-shaped waves with kink and rogue properties. These structures help in explaining how bacterial populations organize and react to stimulation. This work employs 3D, contour, and density plots to reveal the complex dynamics of such structures. In a nutshell, this work gives new a perspective into the physical behavior of bacterial colonies and contributes to a broader understanding of pattern formation in biological systems with potential relevance to ecological and evolutionary studies.