Integrable Nonlinear Wave Equations and Possible Connections to Tsunami Dynamics
In this article we present a brief overview of the nature of localized solitary wave structures/solutions underlying integrable nonlinear dispersive wave equations with specific reference to shallow water wave propagation and explore their possible connections to tsunami waves. In particular, we will discuss the derivation of Korteweg-de Vries family of soliton equations in unidirectional wave propagation in shallow waters and their integrability properties and the nature of soliton collisions.
KeywordsSolitary Wave Tsunami Wave Solitary Wave Solution Shallow Water Wave Cnoidal Wave
Unable to display preview. Download preview PDF.
- Ram Mohan V etal (2006) Impact of South Asian Tsunami on 26 December 2004 on south east coast of India-A field report (preprint)Google Scholar
- Dudley WC and Min L (1988) Tsunami!. Honolulu, Hawaii: Univeristy of Hawaii pressGoogle Scholar
- Okada Y (1985) Surface deformation due to sheer and tensile fault in a half space. Bull Seism Soc Am 82:1135–54Google Scholar
- See for example, Bullough RK (1988) The wave par excellence: the solitary progressive great wave of equilibrium of the fluid-an early history of solitary wave. In: Lakshmanan M (Ed.) Solitons: Introduction and applications. Springer, BerlinGoogle Scholar
- Kortweg DJ and de Vries D (1895) On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Phil Mag 39:422–443Google Scholar
- Lakshmanan M and Rajasekar S (2003) Nonlinear Dynamics: Integrability, Chaos and Patterns. Springer, BerlinGoogle Scholar
- Ablowitz MJ and Clarkson PA (1991) Solitons, Nonlinear evolution equations and inverse scattering. Cambridge University Press, CambridgeGoogle Scholar
- Calogero F and Degasperis A (1982) Spectral transform and solitons. North-Holland, AmsterdamGoogle Scholar
- Caputo JG and Stepanyants YA (2003) Bore formation, evolution and disintegration into solitons in shallow inhomogeneous channels. Nonlinear Processes in Geophysics 10:407–24Google Scholar