Propagation of Water Waves over Uneven Bottom under the Effect of Surface Tension. (30th September 2015)

• Record Type: Journal Article
• Authors: Muñoz Grajales, Juan Carlos
• Other Names: Humi Mayer Academic Editor.
• Is Part Of: International journal of differential equations. Volume 2015(2015)
• Publication Date: 2015-09-30
• Subjects: Differential equations -- Periodicals; Differential equations; Periodicals; 515.35
• DOI: 10.1155/2015/805625
• Languages: English
• ISSNs: 1687-9643

Abstract

Abstract : We establish existence and uniqueness of solutions to the Cauchy problem associated with a new one-dimensional weakly-nonlinear, weakly-dispersive system which arises as an asymptotical approximation of the full potential theory equations for modelling propagation of small amplitude water waves on the surface of a shallow channel with variable depth, taking into account the effect of surface tension. Furthermore, numerical schemes of spectral type are introduced for approximating the evolution in time of solutions of this system and its travelling wave solutions, in both the periodic and nonperiodic case.