Hc. Lei, GROUP SPLITTING AND LINEARIZATION MAPPING OF A SOLVABLE NONLINEAR-WAVE EQUATION, International journal of non-linear mechanics, 33(3), 1998, pp. 461-471
This study explores the infinite group structures related to integrabi
lities of a solvable wave equation proposed by Calogero. We find the g
roup splittings as well as the linearization mapping of the equation a
nd its equivalent system. The equivalent system is found to be an auto
morphic system with respect to an infinite group. It can also be split
into an automorphic system and a resolving system which can be solved
by quadratures. In English literature a concrete example is difficult
to find that illustrates the notion of reducing a non-linear PDE with
order higher than one to quadratures by the method of group splitting
. Our results indicate that the equivalent system can be served as a g
ood example in this aspect. The results obtained also provide a group-
theoretic interpretation of the solvability of the equation, which had
not been completely developed in Calogero's original work. Since the
equation does not pass the Painleve test, our results demonstrate that
sometimes group analysis can obtain much more information than the Pa
inleve test does in detecting the integrabilities of non-linear PDEs.
(C) 1997 Elsevier Science Ltd.