1996/05/01 by A. Ludu, R. A. Ionescu, W. Greiner · 2 citations
Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #Fluid Dynamics and Thin Films #Nonlinear Waves and Solitons #Ocean Waves and Remote Sensing #math.QA #nlin.PS #patt-sol #q-alg
paper · pdf · doi:10.1007/bf02058238
published as Found. Phys. 26 (1996) 665-678 · 17 pages, Latex, PACS: 47.20.Ky, 43.25.Rq, 47.35.+i, 03.40.Kf, 43.25.Fe, 02.20.Tw, MSC: 16W30, 17B37, 81R50, 35Q51, 34B15, 34L30, 76E30
openalex publication_date 1996/05/01 · arxiv created 1996/12/03 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We generalize the non-linear one-dimensional equation of a fluid layer for any depth and length as an infinite order differential equation for the steady waves. This equation can be written as a q-differential one, with its general solution written as a power series expansion with coefficients satisfying a nonlinear recurrence relation. In the limit of long and shallow water (shallow channels) we reobtain the well known Korteweg-de-Vries equation together with its single-soliton solution.