Physica A 249 (1998) 10–17 Propagating solitary states in highly dissipative driven uids J. Fineberg ∗ , O. Lioubashevski The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel Abstract Highly localized solitary states, driven by means of the spatially uniform, vertical acceleration of a thin uid layer, are observed to propagate along the 2D surface of a uid in a highly dissipative regime. Unlike classical solitons, these states propagate at a single constant velocity for given uid parameters and their existence is dependent on the highly dissipative character of the system. The properties of these states are discussed and examples of bound states and two-state interactions are presented. c  1998 Elsevier Science B.V. All rights reserved. Highly localized states have long captured the imagination of Physicists in disciplines ranging from solid state to high-energy physics. Non-linear systems, in particular, have an inherent ability for self-organization or self-focusing that, in many cases, gives rise to these intriguing states. A classic example is the soliton, rst documented by Rus- sell [1], as he chased it on horseback through the canals of 19th century Scotland. Soliton-type structures have since been observed in a wide class of conservative or nearly conservative non-linear systems where the balance between non-linear ampli- cation and dispersion can give rise to stable, highly localized structures. We now pose the question of whether these types of structures can exist in dissipative systems. Localized, soliton-like structures, ubiquitous in 1D non-linear integrable systems, are rarely if at all observed in highly dissipative 2D or 3D systems. Recent studies of 1D classical conservative systems show that dissipation strongly inuences solitons. In extensions of the Kuramoto–Sivashinsky (KS) and KdV equations [2], although soliton-like solutions were seen to persist, the addition of slight dissipative eects was enough to cause the collapse of a family of solitons having a continuum of propaga- tion velocities to a single selected state. Highly localized soliton-like states have also been observed as stable solutions of dissipative subcritical complex Ginzburg–Landau equations with fth-order damping terms. In these 2D systems both stationary [3] and * Corresponding author. 0378-4371/98/$19.00 Copyright c  1998 Elsevier Science B.V. All rights reserved PII S0378-4371(97)00426-3