Solitary wave solutions to a class of Whitham?Boussinesq systems
Peer reviewed, Journal article
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Original versionZeitschrift für Angewandte Mathematik und Physik. 2019, 70 (3), 1-13. 10.1007/s00033-019-1116-0
In this note, we study solitary wave solutions of a class of Whitham–Boussinesq systems which include the bidirectional Whitham system as a special example. The travelling wave version of the evolution system can be reduced to a single evolution equation, similar to a class of equations studied by Ehrnström et al. (Nonlinearity 25:2903–2936, 2012). In that paper, the authors prove the existence of solitary wave solutions using a constrained minimization argument adapted to noncoercive functionals, developed by Buffoni (Arch Ration Mech Anal 173:25–68, 2004), Groves and Wahlén (J Math Fluid Mech 13:593–627, 2011), together with the concentration–compactness principle.