
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 pionnucleon scattering with ($3\times3$) crossing symmetry matrix are investigated in the wellknown 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 wellknown 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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Theoretical and Mathematical Physics, 1982, 50:2, 164–170
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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
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\by K.~V.~Rerikh
\paper ChewLow equations as cremona transformations structure of general intgrals
\jour TMF
\yr 1982
\vol 50
\issue 2
\pages 251260
\mathnet{http://mi.mathnet.ru/tmf2107}
\mathscinet{http://www.ams.org/mathscinetgetitem?mr=662041}
\transl
\jour Theoret. and Math. Phys.
\yr 1982
\vol 50
\issue 2
\pages 164170
\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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http://mi.mathnet.ru/eng/tmf2107 http://mi.mathnet.ru/eng/tmf/v50/i2/p251
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This publication is cited in the following articles:

A. P. Veselov, “Integrable maps”, Russian Math. Surveys, 46:5 (1991), 1–51

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

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