Investigating overtaking collisions of solitary waves in the Schamel equation

Marcelo V. Flamarion, Efim Pelinovsky and Ekaterina Didenkulova

Chaos, Solitons & Fractals, 2023, vol. 174, issue C

Abstract: This article presents a numerical investigation of overtaking collisions between two solitary waves in the context of the Schamel equation. Our study reveals different regimes characterized by the behavior of the wave interactions. In certain regimes, the collisions maintain two well-separated crests consistently over time, while in other regimes, the number of local maxima undergoes variations following the patterns of 2→1→2→1→2 or 2→1→2. These findings demonstrate that the geometric Lax-categorization observed in the Korteweg–de Vries equation (KdV) for two-soliton collisions remains applicable to the Schamel equation. However, in contrast to the KdV, we demonstrate that an algebraic Lax-categorization based on the ratio of the initial solitary wave amplitudes is not feasible for the Schamel equation. Additionally, we show that the statistical moments for two-solitary wave collisions are qualitatively similar to the KdV equation and the phase shifts after soliton interactions are close to ones in integrable KdV and modified KdV models.

Keywords: Solitary waves; Collisions; Schamel equation (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007713

DOI: 10.1016/j.chaos.2023.113870

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