Instability of solitary waves for a generalized Benney–Luke equation

We study linear instability of solitary wave solutions of a one-dimensional generalized Benney–Luke equation, which is a formally valid approximation for describing two-way water wave propagation in the presence of surface tension. Further, we implement a finite difference numerical scheme which com...

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Veröffentlicht in:	Nonlinear analysis 2008-05, Vol.68 (10), p.3009-3033
Hauptverfasser:	Quintero, José Raúl, Muñoz Grajales, Juan Carlos
Format:	Artikel
Sprache:	eng
Schlagworte:	Boussinesq equation Eigenvalue problem Exact sciences and technology Linear instability Mathematical analysis Mathematics Sciences and techniques of general use Solitary wave
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Beschreibung
Zusammenfassung:	We study linear instability of solitary wave solutions of a one-dimensional generalized Benney–Luke equation, which is a formally valid approximation for describing two-way water wave propagation in the presence of surface tension. Further, we implement a finite difference numerical scheme which combines an explicit predictor and an implicit corrector step to compute solutions of the model equation which is used to validate the theory presented.
ISSN:	0362-546X 1873-5215
DOI:	10.1016/j.na.2007.02.042