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Rational Solutions to the ABS List: Transformation Approach

Rational solutions to the ABS list: transformation approach
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 02 Oct 2017Embargo end date: 01 Jan 2017Publisher:SIGMA (Symmetry, Integrability and Geometry: Methods and Application)Journal:Symmetry, Integrability and Geometry: Methods and Applications (eissn: 1815-0659, Copyright policy )
Authors: Zhang, D.; Zhang, D.J.;

doi: 10.3842/sigma.2017.078 , 10.48550/arxiv.1702.01266

arXiv: 1702.01266

Rational Solutions to the ABS List: Transformation Approach

Abstract

In the paper we derive rational solutions for the lattice potential modified Korteweg-de Vries equation, and Q2, Q1($��$), H3($��$), H2 and H1 in the Adler-Bobenko-Suris list. B��cklund transformations between these lattice equations are used. All these rational solutions are related to a unified $��$ function in Casoratian form which obeys a bilinear superposition formula.

Related Organizations
Keywords

Soliton equations, KdV equations (Korteweg-de Vries equations), rational solutions, Nonlinear Sciences - Exactly Solvable and Integrable Systems, NLS equations (nonlinear Schrödinger equations), ABS list, Casoratian, FOS: Physical sciences, Bäcklund transformation, Exactly Solvable and Integrable Systems (nlin.SI)

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    popularity
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Average
Average
Average
Green
gold