Advances in Differential Equations

Existence and non existence of solitons for a 1D Benney-Luke model of higher order

Octavio Montoya and José R. Quintero

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We shall establish the existence and non existence of solitons (travelling waves of finite energy) for a Benney-Luke equation of higher order, which includes models for long water waves with small amplitude. Following a variational approach, solitons are characterized as critical points of the action functional. Existence of solitons follows by the Concentration-Compactness principle by P.-L. Lions, applied to an appropriated minimization problem. It is also shown that solitons are smooth.

Article information

Adv. Differential Equations, Volume 20, Number 11/12 (2015), 1187-1220.

First available in Project Euclid: 18 August 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q35: PDEs in connection with fluid mechanics 35B35: Stability 76B25: Solitary waves [See also 35C11]


Quintero, José R.; Montoya, Octavio. Existence and non existence of solitons for a 1D Benney-Luke model of higher order. Adv. Differential Equations 20 (2015), no. 11/12, 1187--1220.

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