title: Jumping solitary waves in an autonomous reaction-diffusion system with subcritical wave instability.
abstract: 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.
authors.affiliation: Department of Chemistry and Volen Center for Complex Systems, MS 015, Brandeis University, Waltham, Massachusetts 02454-9110, USA.
authors.forename: Lingfa
authors.initials: L
authors.lastname: Yang
authors.forename: Anatol M
authors.initials: AM
authors.lastname: Zhabotinsky
authors.forename: Irving R
authors.initials: IR
authors.lastname: Epstein
mesh_terms: 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*
chemical_list: D012996:Solutions