Analytical solutions of long nonlinear internal waves: Part I

Samir Hamdi (), Brian Morse, Bernard Halphen and William Schiesser

Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, 2011, vol. 57, issue 3, 597-607

Abstract: The Gardner equation is an extension of the Korteweg–de Vries (KdV) equation. It exhibits basically the same properties as the classical KdV, but extends its range of validity to a wider interval of the parameters of the internal wave motion for a given environment. In this paper, we derive exact solitary wave solutions for the generalized Gardner equation that includes nonlinear terms of any order. Unlike previous studies, the exact solutions are derived without assuming their mathematical form. Illustrative examples for internal solitary waves are also provided. The traveling wave solutions can be used to specify initial data for the incident waves in internal waves numerical models and for the verification and validation of the associated computed solutions. Copyright Springer Science+Business Media B.V. 2011

Keywords: Extended KdV equation; Generalized Gardner equation; Cubic nonlinearity; Internal waves; Solitary waves (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:nathaz:v:57:y:2011:i:3:p:597-607

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DOI: 10.1007/s11069-011-9757-0

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