Nonlocal symmetries related to Bäcklund transformation and their applications

By S. Lou, Xiaorui Hu, Yong Chen. 2012

204 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Spectroscopy, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a110370adefc7c0db46f6003487d31377161b363

Citations in the corpus

• Lie symmetries and nonlocally related systems of the continuous and discrete dispersive long waves system by geometric approach (2015, unknown): “[7, 23, 28, 29] have studied symmetry reductions of the Lax pairs for some (2+1)-dimensional equations.”