Method of local construction of invariant subspaces in the solution space of Chew--Low equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 3 (1970) no. 1, pp. 78-93
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A nonlinear system offunctlonal equations for the matrix elements of the $S$-matrix is formulated on the basis of Chew–Low equations. A transition is made to projective coordinates in the spade of the matrix elements of the $S$-matrix and the unitarity condiflons are linearlzed. On the basis of a geometrical interpretation of the system of nonlinear functional
equations as a transformation in an $(n-1)$-dimensional real space, it is shown
that some of the solutions of the original system of equations lie on invariant hypersurfaecs of this space. A method is proposed for the local construction of the invariant hypersurfaces in the neighborhood of the fixed points of the transformation. This method is applied to the Chew–Low equations with $3\times 3$ and $4\times 4$ crossing matrices. It is shown that, if the Chew–Low equations have a selution, the arbitrariness, which is a generalization of
the well-known $\beta$-arbitrariness, in the solutions of the class considered is not exhaustive.
@article{TMF_1970_3_1_a5,
author = {V. A. Meshcheryakov and K. V. Rerikh},
title = {Method of local construction of invariant subspaces in the solution space of {Chew--Low} equations},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {78--93},
publisher = {mathdoc},
volume = {3},
number = {1},
year = {1970},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1970_3_1_a5/}
}
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%0 Journal Article %A V. A. Meshcheryakov %A K. V. Rerikh %T Method of local construction of invariant subspaces in the solution space of Chew--Low equations %J Teoretičeskaâ i matematičeskaâ fizika %D 1970 %P 78-93 %V 3 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1970_3_1_a5/ %G ru %F TMF_1970_3_1_a5
V. A. Meshcheryakov; K. V. Rerikh. Method of local construction of invariant subspaces in the solution space of Chew--Low equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 3 (1970) no. 1, pp. 78-93. http://geodesic.mathdoc.fr/item/TMF_1970_3_1_a5/