Advances in Differential Equations

Existence and asymptotic properties of solitary-wave solutions of Benjamin-type equations

Jerry L. Bona and Hongqiu Chen

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Benjamin recently put forward a model equation for the evolution of waves on the interface of a two-layer system of fluids in which surface tension effects are not negligible. It is our purpose here to investigate the solitary-wave solutions of Benjamin's model. For a class of equations that includes Benjamin's model featuring conflicting contributions to dispersion from dynamic effects on the interface and surface tension, we establish existence of travelling-wave solutions. Using the recently developed theory of Li and Bona, we are also able to determine rigorously the spatial asymptotics of these solutions.

Article information

Adv. Differential Equations, Volume 3, Number 1 (1998), 51-84.

First available in Project Euclid: 19 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 76B25: Solitary waves [See also 35C11]
Secondary: 35Q35: PDEs in connection with fluid mechanics 76B45: Capillarity (surface tension) [See also 76D45] 76C10


Chen, Hongqiu; Bona, Jerry L. Existence and asymptotic properties of solitary-wave solutions of Benjamin-type equations. Adv. Differential Equations 3 (1998), no. 1, 51--84.

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