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SIGMA, 2017, Volume 13, 078, 24 pages (Mi sigma1278)  

This article is cited in 5 scientific papers (total in 5 papers)

Rational Solutions to the ABS List: Transformation Approach

Danda Zhang, Zhang Da-Jun

Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China

Abstract: In the paper we derive rational solutions for the lattice potential modified Korteweg–de Vries equation, and $\mathrm{Q2}$, $\mathrm{Q1}(\delta)$, $\mathrm{H3}(\delta)$, $\mathrm{H2}$ and $\mathrm{H1}$ in the Adler–Bobenko–Suris list. Bäcklund transformations between these lattice equations are used. All these rational solutions are related to a unified $\tau$ function in Casoratian form which obeys a bilinear superposition formula.

Keywords: rational solutions; Bäcklund transformation; Casoratian; ABS list.

Funding Agency Grant Number
National Science Foundation 11371241
11631007
This project is supported by the NSF of China (no. 11371241 and no. 11631007).


DOI: https://doi.org/10.3842/SIGMA.2017.078

Full text: PDF file (500 kB)
Full text: http://www.emis.de/.../078
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Bibliographic databases:

MSC: 35Q51; 35Q55
Received: March 21, 2017; in final form September 26, 2017; Published online October 2, 2017
Language:

Citation: Danda Zhang, Zhang Da-Jun, “Rational Solutions to the ABS List: Transformation Approach”, SIGMA, 13 (2017), 078, 24 pp.

Citation in format AMSBIB
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\by Danda~Zhang, Zhang~Da-Jun
\paper Rational Solutions to the ABS List: Transformation Approach
\jour SIGMA
\yr 2017
\vol 13
\papernumber 078
\totalpages 24
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\crossref{https://doi.org/10.3842/SIGMA.2017.078}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85031314512}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. W. Feng, S.-L. Zhao, “Oscillatory solutions for lattice Korteweg-de Vries-type equations”, Z. Naturfors. Sect. A-J. Phys. Sci., 73:2 (2018), 91–98  crossref  isi
    2. D. Zhang, Da-jun Zhang, “On decomposition of the ABS lattice equations and related Bäcklund transformations”, J. Nonlinear Math. Phys., 25:1 (2018), 34–53  crossref  mathscinet  isi
    3. Zhao S.-l. Zhang D.-j., “Rational Solutions to Q3(Delta) in the Adler-Bobenko-Suris List and Degenerations”, J. Nonlinear Math. Phys., 26:1 (2019), 107–132  crossref  mathscinet  zmath  isi  scopus
    4. Cheng Q., Zhang Ch., Zhang D., Zhang D.-j., “On One-Soliton Solutions of the Q2 Equation in the Abs List”, Adv. Differ. Equ., 2019, 30  crossref  mathscinet  isi  scopus
    5. Zhang D., Zhang D.-j., “Addition Formulae, Backlund Transformations, Periodic Solutions, and Quadrilateral Equations”, Front. Math. China, 14:1 (2019), 203–223  crossref  mathscinet  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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