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SIGMA, 2013, Volume 9, 006, 13 pages (Mi sigma789)  

This article is cited in 3 scientific papers (total in 3 papers)

On the $N$-Solitons Solutions in the Novikov–Veselov Equation

Jen-Hsu Chang

Department of Computer Science and Information Engineering, National Defense University, Tauyuan, Taiwan

Abstract: We construct the $N$-solitons solution in the Novikov–Veselov equation from the extended Moutard transformation and the Pfaffian structure. Also, the corresponding wave functions are obtained explicitly. As a result, the property characterizing the $N$-solitons wave function is proved using the Pfaffian expansion. This property corresponding to the discrete scattering data for $N$-solitons solution is obtained in [arXiv:0912.2155] from the $\overline\partial$-dressing method.

Keywords: Novikov–Veselov equation; $N$-solitons solutions; Pfaffian expansion; wave functions

DOI: https://doi.org/10.3842/SIGMA.2013.006

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Full text: http://emis.mi.ras.ru/.../006
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Bibliographic databases:

ArXiv: 1206.3751
MSC: 35C08; 35A22
Received: October 1, 2012; in final form January 12, 2013; Published online January 20, 2013
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Citation: Jen-Hsu Chang, “On the $N$-Solitons Solutions in the Novikov–Veselov Equation”, SIGMA, 9 (2013), 006, 13 pp.

Citation in format AMSBIB
\Bibitem{Cha13}
\by Jen-Hsu~Chang
\paper On the $N$-Solitons Solutions in the Novikov--Veselov Equation
\jour SIGMA
\yr 2013
\vol 9
\papernumber 006
\totalpages 13
\mathnet{http://mi.mathnet.ru/sigma789}
\crossref{https://doi.org/10.3842/SIGMA.2013.006}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3033548}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84872773416}


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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. Jen-Hsu Chang, “Mach-Type Soliton in the Novikov–Veselov Equation”, SIGMA, 10 (2014), 111, 14 pp.  mathnet  crossref
    2. Chang J.-H., “The interactions of solitons in the Novikov–Veselov equation”, Appl. Anal., 95:6 (2016), 1370–1388  crossref  mathscinet  zmath  isi  elib  scopus
    3. Zhu N., Pan Ch., Liu Zh., “Two kinds of important bifurcation phenomena of nonlinear waves in a generalized Novikov–Veselov equation”, Nonlinear Dyn., 83:3 (2016), 1311–1324  crossref  mathscinet  zmath  isi  elib  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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