On the Stability of Kink-Like and Soliton-Like Solutions of the Generalized Convection-Reaction-Diffusion Equation

Abstract

Stability of the kink-like and soliton-like travelling wave solutions to the generalized convection-reaction-diffusion equation is studied by means of the qualitative methods and numerical simulation.

Solitary Waves in the Model of Active Media, Taking into Account Effects of Relaxation

“…( 5), are investigated in [22,23,24,25], where a number of solitary wave solutions have been described. Yet the analytical study as well as the numerical investigations show that none of the solitary wave solution is stable [26] in absence of kinetic equations.…”

“…j=1 lie in the left half-plane of the complex plane. Unfortunately, we do not have a suffice evidence on that λ j (k) ⊂ C − , and we treat the inequalities (26) as conjectures that should be verified numerically (cf. with Figure 4).…”

“…In studying the spectral stability of the TW solutions (u c (z), w c (z)), we examine the existence of nontrivial solutions to (23), (24) with Re(λ) > 0, treating the inequalities (26) as the only one possible arrangement of the roots of the characteristic polynomial W λ (β).…”