https://doi.org/10.1140/epjp/i2016-16425-7
Regular Article
The nonlinear dispersive Davey-Stewartson system for surface waves propagation in shallow water and its stability
1
Faculty of Mathematics and Statistics, Central China Normal University, 430079, Wuhan, China
2
Mathematics Department, Faculty of Science, Menoufia University, 32511, Shebin El-kom, Egypt
3
Mathematics Department, Faculty of science, Taibah University, Al-Ula, Saudi Arabia
4
Mathematics Department, Faculty of Science, Beni-Suef University, Beni Suef, Egypt
* e-mail: aly742001@yahoo.com
Received:
31
August
2016
Accepted:
11
November
2016
Published online:
9
December
2016
The three-dimensional (3-D) nonlinear and dispersive PDEs system for surface waves propagating at undisturbed water surface under the gravity force and surface tension effects are studied. By applying the reductive perturbation method, we derive the (2 + 1) -dimensions form of the Davey-Stewartson (DS) system for the modulation of 2-D harmonic waves. By using the simplest equation method, we find exact traveling wave solutions and a general form of the multiple-soliton solution of the DS model. The dispersion analysis as well as the conservation law of the DS system are discussed. It is revealed that the consistency of the results with the conservation of the potential energy increases with increasing Ursell parameter. Also, the stability of the ODEs form of the DS system is presented by using the phase portrait method.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2016
