caa a22 4500 475797256 CHVBK 20180406123728.0 cr unu---uuuuu 170329e20000901xx s 000 0 eng 10.1007/PL00001513 doi (NATIONALLICENCE)springer-10.1007/PL00001513 Jones M. C. W. Department of Pure Mathematics, The Queen's University of Belfast, Belfast BT7 1NN, UK, Fax: +44 01232 335076, UK aut A codimension seven unfolding of a third harmonic resonant interaction between two contiguous continua [Elektronische Daten] [M. C. W. Jones] Abstract.: In this paper we study the capillary-gravity profiles which may occur at the interface of two fluids when the fundamental mode and its third harmonic interact with each other. The problem is treated as one in bifurcation theory by transforming it into a nonlinear operator equation between suitable function spaces. Using classical analytic methods and by exploiting the group invariances of the operator, we are able to describe the solution set of the equation for a selection of values of the parameters present and to allow for possible imperfections in the resonance. Birkhäuser Verlag, Basel,, 2000 Key words. Capillary-gravity, mode interaction, O(2)-invariance, bifurcation, Lyapunov-Schmidt, universal unfolding nationallicence https://doi.org/10.1007/PL00001513 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/PL00001513 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Jones M. C. W. Department of Pure Mathematics, The Queen's University of Belfast, Belfast BT7 1NN, UK, Fax: +44 01232 335076, UK aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer