Painlevé analysis and exact solutions for the Belousov–Zhabotinskii reaction–diffusion system

Analytical properties and exact solutions of the Lotka–Volterra competition system

“…(the Kudryashov method). This method has some advantages that were discussed in recent papers [38][39][40][41]. It was found that both equations in system (7) have the second order pole, therefore we seek solutions of this system in the following form:…”

“…Substitute (40) into (37) and take into account expressions (38) and (39) for the derivatives of ℘(z). So, we have a polynomial for the function ℘(z).…”

“…(the Kudryashov method). This method has some advantages that were discussed in recent papers [38][39][40][41].…”

Probing the oscillating Belousov-Zhabotinskii reaction with micrometer-sized electrodes: the effect of C, Pt, and Au

“…The model introduced by Györgyi and co-workers contains at least 80 elementary reactions and 26 species of variable concentration [25]. More recently, efforts have included finding an exact solution for the concentration wave [27]. Other studies of the BZ reaction in a batch reactor were performed that included the development of a model that allowed variations of the reactant concentrations [28].…”