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TMF, 2012, Volume 171, Number 2, Pages 241–253 (Mi tmf8367)  

This article is cited in 7 scientific papers (total in 7 papers)

Another new goldfish model

F. Calogeroab

a National Institute of Nuclear Physics, Sezione di Roma, Roma, Italy
b Physics Department, University of Rome "La Sapienza", Roma, Italy

Abstract: A new integrable (indeed, solvable) model of goldfish type is identified, and some of its properties are discussed. Its Newtonian equations of motion read as follows:
\begin{align*} \ddot z_n= &\frac{\dot z_n^2}{z_n}+c_1\frac{\dot z_n}{z_n}+ c_2\dot z_n+c_2c_3z_n+c_1c_2+
[2mm] & +\sum_{m=1,m\ne n}^N\frac{(\dot z_n+c_3z_n+c_1)(\dot z_m+c_3z_m+c_1)} {z_m}\cdot\frac{z_n+z_m}{z_n-z_m},\quad n=1,…,N, \end{align*}
where $c_1$, $c_2$, and $c_3$ are arbitrary constants, $z_n\equiv z_n(t)$ are the $N$ dependent variables, $N$ is an arbitrary positive number $(N>1)$, $t$ is the independent variable {(}“time”{\rm)} and the dots indicate time-differentiations.

Keywords: integrable dynamical systems, solvable dynamical systems, integrable Newtonian many-body problems

DOI: https://doi.org/10.4213/tmf8367

Full text: PDF file (481 kB)
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English version:
Theoretical and Mathematical Physics, 2012, 171:2, 629–640

Bibliographic databases:

Received: 17.05.2012

Citation: F. Calogero, “Another new goldfish model”, TMF, 171:2 (2012), 241–253; Theoret. and Math. Phys., 171:2 (2012), 629–640

Citation in format AMSBIB
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\by F.~Calogero
\paper Another new goldfish model
\jour TMF
\yr 2012
\vol 171
\issue 2
\pages 241--253
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\transl
\jour Theoret. and Math. Phys.
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\pages 629--640
\crossref{https://doi.org/10.1007/s11232-012-0060-3}
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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. Francesco Calogero, “Another new solvable many-body model of goldfish type”, SIGMA, 8 (2012), 046, 17 pp.  mathnet  crossref  mathscinet
    2. F. Calogero, “On a technique to identify solvable discrete-time many-body problems”, Theoret. and Math. Phys., 172:2 (2012), 1052–1072  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    3. Francesco Calogero, Ge Yi, “A new class of solvable many-body problems”, SIGMA, 8 (2012), 066, 29 pp.  mathnet  crossref  mathscinet
    4. Calogero F., “Two quite similar matrix ODEs and the many-body problems related to them”, Int. J. Geom. Methods Mod. Phys., 9:2 (2012), 1260002, 6 pp.  crossref  mathscinet  isi  elib  scopus
    5. Calogero F., “New solvable many-body model of Goldfish type”, J. Nonlinear Math. Phys., 19:1 (2012), 1250006, 19 pp.  crossref  mathscinet  zmath  isi  scopus
    6. Oksana Bihun, Francesco Calogero, “Solvable Many-Body Models of Goldfish Type with One-, Two- and Three-Body Forces”, SIGMA, 9 (2013), 059, 18 pp.  mathnet  crossref  mathscinet
    7. Bihun O., Calogero F., “Equilibria of a Solvable N-Body Problem and Related Properties of the N Numbers X(N) at Which the Jacobi Polynomial of Order N Has the Same Value”, J. Nonlinear Math. Phys., 20:4 (2013), 539–551  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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