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TMF, 1982, Volume 50, Number 2, Pages 251–260 (Mi tmf2107)  

This article is cited in 2 scientific papers (total in 2 papers)

Chew–Low equations as cremona transformations structure of general intgrals

K. V. Rerikh


Abstract: The Chew–Low equations for the $p$ waves of pion-nucleon scattering with ($3\times3$) crossing symmetry matrix are investigated in the well-known form of a nonlinear system of difference equations. It is shown these equations, interpreted as geometrical transformations, are a special case of Cremona transformations. Using the properties of Cremona transformations, we obtain general functional equations, which depend on three parameters, for algebraic and nonalgebraic invariant curves in the space of solutions of the Chew–Low equations. It is shown that there is only one algebraic invariant curve, a parabola corresponding to the well-known solution. Analysis of the general functional equation for nonalgebraic invariant curves shows that besides this parabola there are three invariant forms which specify implicitly three nonalgebraic curves: a general equation for them is found by fixing the parameters. An important result follows from the transformation properties of these invariant forms with respect to Cremona transformations, namely, the ratio of these forms to appropriate powers is a general integral of the nonlinear system of Chew–Low equations: it is an even antiperiodic function. The structure of a second general integral and the functional equation of which it is a solution are given.

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English version:
Theoretical and Mathematical Physics, 1982, 50:2, 164–170

Bibliographic databases:

Received: 01.12.1980

Citation: K. V. Rerikh, “Chew–Low equations as cremona transformations structure of general intgrals”, TMF, 50:2 (1982), 251–260; Theoret. and Math. Phys., 50:2 (1982), 164–170

Citation in format AMSBIB
\Bibitem{Rer82}
\by K.~V.~Rerikh
\paper Chew--Low equations as cremona transformations structure of general intgrals
\jour TMF
\yr 1982
\vol 50
\issue 2
\pages 251--260
\mathnet{http://mi.mathnet.ru/tmf2107}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=662041}
\transl
\jour Theoret. and Math. Phys.
\yr 1982
\vol 50
\issue 2
\pages 164--170
\crossref{https://doi.org/10.1007/BF01015297}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1982PH72200007}


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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. A. P. Veselov, “Integrable maps”, Russian Math. Surveys, 46:5 (1991), 1–51  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. K. V. Rerikh, “General Approach to Integrating Invertible Dynamical Systems Defined by Transformations from the Cremona group $\operatorname{Cr}(P^n_k)$ of Birational Transformations”, Math. Notes, 68:5 (2000), 594–601  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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