We provide the first construction of exact solitary waves of large amplitude with an arbitrary distribution of vorticity. We use continuation to construct a global connected set of symmetric solitary waves of elevation, whose profiles decrease monotonically on either side of a central crest. This generalizes the classical result of Amick and Toland.

Node Department(s) People Bath Maths Graham, Spence, Smyshlyaev, Toland Cardiff & Liverpool Engineering, Maths Levitin, McWhirter, Marletta, Maz’ya KCL and UCL Maths Davies, Shargorodsky, Parnovski Lancaster Physics Burton, Tucker Birmingham & Manchester Maths Betcke, Chahlaoui, Higham, Mathias, Mehl, Tisseur Nottingham Engineering Garvey, Popov, Prells Reading Maths Chandler-Wilde, Kondratiev,...

A general abstract duality result is proposed for equations which are governed by the sum of two operators (possibly multivalued). It allows to unify a large number of variational duality principles, including the Clarke-Ekeland least dual action principle and the Singer-Toland duality. Moreover, it offers a new duality approach to some central questions in the theory of variational inequalitie...