Proceedings of the Conference on Nonlinear Coherent Structures in Physics and Biology,
Heriot-Watt University, Edinburgh, July 95

The Dirac equation and the Davey-Stewartson I equation: deformation of the dromion solutions

M. Mañas

Departamento de Física Teórica,
Universidad Complutense, Spain


Our contribution to this conference regards some of the recent results obtained jointly with F. Guil, which can be found in the papers The Dirac Equation and Integrable Systems of KP Type submitted to J. Phys. A: Math. & Gen. and Deformation of the Dromion and Solitoff Solutions of the Davey-Stewartson I Equation submitted to Phys. Lett. A. We summarize these results: The propagator for the 2D heat equation in an arbitrary linear space give solutions of the two-component Kadomtsev-Petviashvilii equations. This propagator is subject to the Klein-Gordon equation and its right-derivatives are required to be of rank-one, that imply that it can be expressed in terms of solutions of the Dirac equation. Large families of solutions of the two-component Kadomtsev-Petviashvilii equations are constructed in terms of solutions of the heat and Dirac equations. Particular attention is paid to the real reductions of the Davey-Stewartson type, recovering in this way the dark line solitons and the multidromion solutions.

A new solution of the Davey-Stewartson I equation is presented. This is a one parameter deformation of the dromion solution, that is contained in as particular example. The deformation corresponding to the 1-dromion solution is studied in detail. We analyze its asymptotic behaviour, appearing as a nonlinear superposition of the 1-dromion with the a 2-line dark soliton type solution. The 1-solitoff degeneration of the 1-dromion and its deformation is studied in a similar fashion. The 1-line dark soliton solution appears as a deformation of the 1-solitoff solution.

Here we present only a part of these results, rather than a full papaer.

Conference paper.


Last modified Mon Apr 8 16:24:59 GB-Eire 1996 (DBD)