Abstract
In this paper we consider dynamical aspects of multi-directional waves described by the Kadomtsev-Petviashvili (KP) equation. We investigate some analytically known solutions: the two-soliton interacting waves and their periodic equivalents. It is shown that the behaviour of the interaction of two-solitons can be classified by a parameter A ≥ 0 (depending on the amplitudes of pure one-solitons and the angles of interactions). In the limiting case when A = 0, it is found that the two-soliton reduces to a three-branch soliton.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Kadomtsev, B.B. & Petviashvili, V.I.: On the stability of solitary waves in weakly dispersive media, Soviet Phys. Dokl. 15(6) (1970), 539–541
Hodnett, P.F. & Moloney, T.P.: On the structure during interaction of the two-soliton of the Korteweg-de Vries equation, SIAM, J. Appl. Math., Vol. 49, 1989.
Miles, J.W.: Obliquely interacting solitary waves, J. Fluid Mech. Vol. 79 part 1 pp. 157–169, 1977.
Segur, H. & Finkel, A.: An Analytical model of periodic waves in shallow water, Studies in applied Mathematics 73, 1985.
Hammack, J.; Scheffner, N., Segur, H.: Two-dimensional periodic waves in shallow water, J. Fluid Mechanics, Vol. 209 pp. 567–589, 1989.
Dubrovin, B.A.: Russian Math. Surveys 36:11–92, 1981
Whitham, G.B.: Linear and Nonlinear Waves J.Wiley, 1974
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Cahyono, E., Van Groesen, E., Soewono, E., Subarinah, S. (1997). Genus-Two Solutions to the Kadomtsev — Petviashvili Equation. In: van Groesen, E., Soewono, E. (eds) Differential Equations Theory, Numerics and Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5157-3_13
Download citation
DOI: https://doi.org/10.1007/978-94-011-5157-3_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6168-1
Online ISBN: 978-94-011-5157-3
eBook Packages: Springer Book Archive