Nonlinear Schrödinger and Davey–Stewartson Equations

Xiaoping Xu
Additional contact information
Xiaoping Xu: Academy of Mathematics and System Science, Institute of Mathematics

Chapter Chapter 6 in Algebraic Approaches to Partial Differential Equations, 2013, pp 179-211 from Springer

Abstract: Abstract The two-dimensional cubic nonlinear Schrödinger equation is used to describe the propagation of an intense laser beam through a medium with Kerr nonlinearity. Coupled two-dimensional cubic nonlinear Schrödinger equations are used to describe the interaction of electromagnetic waves with different polarizations in nonlinear optics. In this chapter, we solve these equations by imposing a quadratic condition on the related argument functions and using their symmetry transformations. More complete families of exact solutions of this type are obtained, many of which are periodic, quasi-periodic, aperiodic, and singular solutions that may have practical significance. The Davey–Stewartson equations are used to describe the long time evolution of three-dimensional packets of surface waves. Assuming that the argument functions are quadratic in spatial variables, we find various exact solutions for the Davey–Stewartson equations.

Keywords: Soliton Solution; Symmetry Transformation; Kerr Nonlinearity; Quadratic Condition; Symmetric Transformation (search for similar items in EconPapers)
Date: 2013
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:978-3-642-36874-5_6

Ordering information: This item can be ordered from
http://www.springer.com/9783642368745

DOI: 10.1007/978-3-642-36874-5_6

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 ().