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TMF, 2003, Volume 137, Number 2, Pages 239–252 (Mi tmf269)  

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

$C$-KP and $B$-KP Equations Related to the Generalized Quartic Hénon–Heiles Hamiltonian

M. Musette, C. Verhoeven

Vrije Universiteit

Abstract: In their classification of soliton equations from a group theoretical standpoint according to the representation of infinite Lie algebras, Jimbo and Miwa listed bilinear equations of low degree for the KP and the modified KP hierarchies. In this list, we consider the $(1+1)$-dimensional reductions of three particular equations of special interest for establishing some new links with the generalized Hénon–Heiles Hamiltonian, possibly useful for integrating the latter with functions having the Painlevé property. Two of those partial differential equations have $N$-soliton solutions that, as for the Kaup–Kupershmidt equation, can be written as the logarithmic derivative of a Grammian. Moreover, they can describe head-on collisions of solitary waves of different type and shape.

Keywords: soliton equations, coupled KdV-type equations, fourth-order Lax pairs, fifth-order Lax pairs, Hamiltonian systems

DOI: https://doi.org/10.4213/tmf269

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English version:
Theoretical and Mathematical Physics, 2003, 137:2, 1561–1573

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Citation: M. Musette, C. Verhoeven, “$C$-KP and $B$-KP Equations Related to the Generalized Quartic Hénon–Heiles Hamiltonian”, TMF, 137:2 (2003), 239–252; Theoret. and Math. Phys., 137:2 (2003), 1561–1573

Citation in format AMSBIB
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\by M.~Musette, C.~Verhoeven
\paper $C$-KP and $B$-KP Equations Related to the Generalized Quartic H\'enon--Heiles Hamiltonian
\jour TMF
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\issue 2
\pages 239--252
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\crossref{https://doi.org/10.4213/tmf269}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2057901}
\zmath{https://zbmath.org/?q=an:1178.35323}
\transl
\jour Theoret. and Math. Phys.
\yr 2003
\vol 137
\issue 2
\pages 1561--1573
\crossref{https://doi.org/10.1023/A:1027318020365}
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  • http://mi.mathnet.ru/eng/tmf/v137/i2/p239

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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. R. Conte, M. Musette, C. Verhoeven, “Completeness of the Cubic and Quartic Henon–Heiles Hamiltonians”, Theoret. and Math. Phys., 144:1 (2005), 888–898  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Conte R, Musette M, Verhoeven C, “Explicit integration of the Henon-Heiles Hamiltonians”, Journal of Nonlinear Mathematical Physics, 12 (2005), 212–227, Suppl. 1  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. Dimakis, A, “BKP and CKP revisited: the odd KP system”, Inverse Problems, 25:4 (2009), 045001  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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