Nonlocal symmetries related to Bäcklund transformation and their applications

Starting from nonlocal symmetries related to Bäcklund transformation (BT), many interesting results can be obtained. Taking the well-known potential KdV (pKdV) equation as an example, a new type of nonlocal symmetry in an elegant and compact form which comes from BT is presented and used to perform...

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Published inJournal of physics. A, Mathematical and theoretical Vol. 45; no. 15; pp. 155209 - 14
Main Authors Lou, S Y, Hu, Xiaorui, Chen, Yong
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 20.04.2012
IOP
Subjects
Backlund transformation
Equivalence
Exact sciences and technology
explicit solution
Group theory
Invariants
Mathematical analysis
Mathematical models
nonlocal symmetry
Physics
potential KdV equation
Symmetry
Transformations (mathematics)
Korteweg-de Vries equation
Invariant
Models
Infinite dimension
Backlund transformation
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Summary:Starting from nonlocal symmetries related to Bäcklund transformation (BT), many interesting results can be obtained. Taking the well-known potential KdV (pKdV) equation as an example, a new type of nonlocal symmetry in an elegant and compact form which comes from BT is presented and used to perform research works in two main subjects: the nonlocal symmetry is localized by introducing suitable and simple auxiliary-dependent variables to generate new solutions from old ones and to consider some novel group invariant solutions; some other models both in finite and infinite dimensions are generated under new nonlocal symmetry. The finite-dimensional models are completely integrable in Liouville sense, which are shown equivalent to the results given through the nonlinearization method for Lax pair.
Bibliography:ObjectType-Article-1
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ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/45/15/155209