The Nonlinear Schrödinger Equation and Solitary Waves

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

Chapter 10 in Nonlinear Partial Differential Equations for Scientists and Engineers, 2012, pp 535-577 from Springer

Abstract: Abstract It has already been indicated in Section 2.3 that the nonlinear Schrödinger (NLS) equation arises in a wide variety of physical problems in fluid mechanics, plasma physics, and nonlinear optics. The most common applications of the NLS equation include self-focusing of beams in nonlinear optics, modeling of propagation of electromagnetic pulses in nonlinear optical fibers which act as wave guides, and stability of Stokes waves in water. Some formal derivations of the NLS equation have been obtained by several methods which include the multiple scales expansions, the asymptotic method, Whitham’s (J. Fluid Mech. 22:273–283, 1965a, Proc. R. Soc. Lond. A283:238–261, 1965b) averaged variational equations, and Phillips’ (J. Fluid Mech. 106:215–227, 1981) resonant interaction equations. Zakharov and Shabat (Sov. Phys. JETP 34:62–69, 1972) developed an ingenious inverse scattering method to show that the NLS equation is completely integrable. The NLS equation is of great importance in adding to our fundamental knowledge of the general theory of nonlinear dispersive waves.

Keywords: Dispersion Relation; Solitary Wave; Soliton Solution; Solitary Wave Solution; Envelope Soliton (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_10

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

DOI: 10.1007/978-0-8176-8265-1_10

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 ().