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Paper IPM / Physic / 7919  


Abstract:  
Recently, it was shown that half BPS Supergravity solution of theories
with SU(24) symmetry algebra is given uniformly by determining a single
function which obeys three dimensional continuous Toda equation. In this
paper, we study the scale invariant solution of Toda equation. Our
motivation is that some solutions of half BPS sector of IIB supergravity,
as one excepts from the fermion description of the theory, are scale
invariant. By defining two auxiliary functions we prove that such
solutions of Toda equation obey cubic algebraic equation. We obtain some
simpl solutions of Toda equation specially, we observe that the PPwave
solution can be written in this fashion.
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