Solitons and the Inverse Scattering Transform

Lokenath Debnath ()
Additional contact information
Lokenath Debnath: University of Texas, Pan American, Department of Mathematics

Chapter 9 in Nonlinear Partial Differential Equations for Scientists and Engineers, 2012, pp 425-533 from Springer

Abstract: Abstract Dispersion and nonlinearity play a fundamental role in wave motions in nature. The nonlinear shallow water equations that neglect dispersion altogether lead to breaking phenomena of the typical hyperbolic kind with the development of a vertical profile. In particular, the linear dispersive term in the Korteweg–de Vries equation prevents this from ever happening in its solution. In general, breaking can be prevented by including dispersive effects in the shallow water theory. The nonlinear theory provides some insight into the question of how nonlinearity affects dispersive wave motions. Another interesting feature is the instability and subsequent modulation of an initially uniform wave profile.

Keywords: Solitary Wave; Travel Wave Solution; Boussinesq Equation; Cnoidal Wave; Peakon Solution (search for similar items in EconPapers)
Date: 2012
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-8265-1_9

Ordering information: This item can be ordered from
http://www.springer.com/9780817682651

DOI: 10.1007/978-0-8176-8265-1_9

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().