1994/12/31 by A. R. Osborne · 15 citations
Earth and Planetary Sciences · Physics and Astronomy · Mathematics · #Ocean Waves and Remote Sensing #Nonlinear Waves and Solitons #Coastal and Marine Dynamics #Korteweg–de Vries equation #Cnoidal wave #Superposition principle #Nonlinear system #Inverse scattering transform #Context (archaeology) #Mathematics #Mathematical analysis #Inverse #Physics #Classical mechanics #Inverse scattering problem #Inverse problem #Wave equation #Geometry #Quantum mechanics
paper · pdf · doi:10.5194/npg-1-241-1994
published in Nonlinear processes in geophysics 1(4), 241-251 (Copernicus Publications)
openalex publication_date 1994/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02
Abstract. The nonlinear dynamics of cnoidal waves, within the context of the general N-cnoidal wave solutions of the periodic Korteweg-de Vries (KdV) and Kadomtsev-Petvishvilli (KP) equations, are considered. These equations are important for describing the propagation of small-but-finite amplitude waves in shallow water; the solutions to KdV are unidirectional while those of KP are directionally spread. Herein solutions are constructed from the 0-function representation of their appropriate inverse scattering transform formulations. To this end a general theorem is employed in the construction process: All solutions to the KdV and KP equations can be written as the linear superposition of cnoidal waves plus their nonlinear interactions. The approach presented here is viewed as significant because it allows the exact construction of N degree-of-freedom cnoidal wave trains under rather general conditions.