Jumping solitary waves in an autonomous reaction-diffusion system with subcritical wave instability.
We describe a new type of solitary waves, which propagate in such a manner that the pulse periodically disappears from its original position and reemerges at a fixed distance. We find such jumping waves as solutions to a reaction-diffusion system with a subcritical short-wavelength instability. We demonstrate closely related solitary wave solutions in the quintic complex Ginzburg-Landau equation. We study the characteristics of and interactions between these solitary waves and the dynamics of related wave trains and standing waves.
Yang
Lingfa
L
Department of Chemistry and Volen Center for Complex Systems, MS 015, Brandeis University, Waltham, Massachusetts 02454-9110, USA.
Zhabotinsky
Anatol M
AM
Epstein
Irving R
IR
D000465:Algorithms; D055592:Biophysical Phenomena; D001703:Biophysics; D004058:Diffusion; D008956:Models, Chemical; D009038:Motion; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*; D012996:Solutions / Q000737:chemistry*
D012996:Solutions