On the Soliton Solutions of the Davey-Stewartson Equation for Long Waves

D. Anker, N. C. Freeman
1978 Proceedings of the Royal Society A  
The D avey-Stew artson equations describe two-dimensional surface waves on w ater of finite depth. In the long wave limit, it is shown th a t these equations belong to the class derivable from operator equations in the manner of Zakharov & Shabat. The basic underlying linear system of equations is obtained and solutions to the original nonlinear system sought from the Gelfand-Levitan equations of Inverse Scattering Theory. Single soliton and multi-soliton solutions are deduced corresponding to
more » ... d corresponding to the one-dimensional solutions already available. The solitons so obtained are pseudo one dimensional in th a t they have the same form as one dimensional solitons b u t move a t an angle to the main direction of propagation. The multi-soliton solution describes the interaction of many such solitons each propagating in different directions. For two soli tons, it is shown th a t resonance occurs and a triple soliton structure is produced.
doi:10.1098/rspa.1978.0083 fatcat:qo6ok3upnnejdl564viz52fk5q