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TMF, 2011, Volume 167, Number 3, Pages 364–376 (Mi tmf6647)  

This article is cited in 9 scientific papers (total in 9 papers)

A new goldfish model

F. Calogeroab

a Nazionale di Fisica Nucleare, 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. A version of its Newtonian equations of motion reads as follows:
$$ \ddot{z}_n=\frac{\beta\dot{z}_n(\dot{z}_n+\eta)}{1+\beta z_n}+ \sum_{m=1,m\ne n}^N\frac{(\dot{z}_n-\beta\eta z_n) (\dot{z}_m-\beta\eta z_m)[2+\beta(z_n+z_m)]} {(z_n-z_m)(1+\beta z_m)}, $$
where $z_n\equiv z_n(t)$ are the $N$ dependent variables, $t$ is the independent variable (“time”), the dots indicate time differentiations, and $\beta$, $\eta$ are two arbitrary constants.

Keywords: integrable dynamical system, solvable dynamical system, integrable Newtonian many-body problem

DOI: https://doi.org/10.4213/tmf6647

Full text: PDF file (458 kB)
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English version:
Theoretical and Mathematical Physics, 2011, 167:3, 714–724

Bibliographic databases:

Received: 23.06.2011

Citation: F. Calogero, “A new goldfish model”, TMF, 167:3 (2011), 364–376; Theoret. and Math. Phys., 167:3 (2011), 714–724

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v167/i3/p364

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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, “Discrete-Time Goldfishing”, SIGMA, 7 (2011), 082, 35 pp.  mathnet  crossref  mathscinet
    2. Calogero F., Yi G., “Can the general solution of the second-order ODE characterizing Jacobi polynomials be polynomial?”, J. Phys. A, 45:9 (2012), 095206, 4 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Calogero F., Yi G., “Diophantine properties of the zeros of certain Laguerre and para-Jacobi polynomials”, J. Phys. A, 45:9 (2012), 095207, 9 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. F. Calogero, “Another new goldfish model”, Theoret. and Math. Phys., 171:2 (2012), 629–640  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. Francesco Calogero, “Another new solvable many-body model of goldfish type”, SIGMA, 8 (2012), 046, 17 pp.  mathnet  crossref  mathscinet
    6. 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
    7. Francesco Calogero, Ge Yi, “A new class of solvable many-body problems”, SIGMA, 8 (2012), 066, 29 pp.  mathnet  crossref  mathscinet
    8. 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
    9. 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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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