# Solitary-like Wave Dynamics in Thin Liquid Films over a Vibrated Inclined Plane
## 1 Introduction  
Solitary waves--physical waves that maintain their shape and move with a constant velocity due to a cancellation of nonlinear effects and dispersive processes in the medium [1]--have been a long-term subject of fundamental and applied research studies in the fields of optics [2], fluid dynamics [3], magnetism [4], acoustics [5], electronics [6], and biology [7, 8]. However, despite a good understanding of the physical properties of solitary waves of different kinds, their experimental studies often involve expensive and difficult-to-operate equipment, such as intense laser beams and nonlinear-optical materials in the field of optics [2] and sources of high-power microwave radiation in the field of magnetism [4]. Yet, in some systems, such as biological nerve fibres [7, 8], the observation of solitary-like waves requires significant preparatory works and is possible mostly when a number of specific experimental conditions are satisfied. Such technical challenges complicate both fundamental studies and the verification of numerous theoretical works predicting that solitary waves could be used in communication [9, 10], sensing [11], and data-processing [12] devices and systems. There also exists a class of material solitary-like surface waves that originate from spatio-temporal evolution of falling liquid films [13, 14]. Since the equipment needed to create falling liquid films is, in general, simpler than that used in experiments in the fields of optics and magnetism, the waves of this kind have attracted the attention of many scientists [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28] following the pioneering experiments conducted by the [PERSON] [29]. In fact, while such solitary-like surface waves share many physical features with the other known types of solitary waves, they can exhibit unique physical properties notobserved in other systems [24; 30; 31]. For instance, they can merge instead of passing through each other without significant change, with the latter being the case of two solitary waves governed by the well-known KdV equation [3; 32]. The analysis of solitary-like surface waves in flowing liquid films is also important because liquid films, as well as similar physical systems [33; 34; 35], are often encountered in the fields of earth and planetary sciences [36; 37] and in technological processes [38], where the liquids of interest can also experience temperature gradients [14; 28] and vibrations [39; 40; 41]. Given this, the effect of vibrations on the wave dynamics of film flows has become an independent subject of fundamental and applied research [42; 43; 44; 45]. In particular, it has been shown that vibrations can suppress certain waves on the surface of flowing liquid films [42] but in a relevant experiment [47] it has been demonstrated that vibrations can promote unusual regimes of spontaneous drop movement. Speaking broadly, the study of the effect of vibrations should also help develop communication, sensing and data processing systems that are immune to undesirable mechanical impacts on devices that use liquids as a medium and provide the critical functionality (see, e.g., [48; 49; 50]). Although, traditionally, greater attention has been paid to the wave dynamics on free-falling vertical liquid films [13; 14], studies of surface waves on liquid films flowing over slightly inclined planes have also been conducted, given them having essentially the same physics as in the case of vertical systems [24; 42]. However, reports on experimental results involving the effect of vibrations are rather scarce and scattered in the literature sources [39; 40; 45]. In particular, in [39] it was shown that the vibration of a horizontal tube with a liquid thin film flowing over it results in the appearance of ripple waves at the vibration frequency. The amplitude of the so-created waves depends on the vibration amplitude and can reach the amplitude of periodic waves existing on the film surface without vibration.