Existence and asymptotic properties of solitary-wave solutions of Benjamin-type equations
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.
Advances in Differential Equations
Chen, H., & Bona, J. (1998). Existence and asymptotic properties of solitary-wave solutions of Benjamin-type equations. Advances in Differential Equations, 3 (1), 51-84. Retrieved from https://digitalcommons.memphis.edu/facpubs/4630