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Paper   IPM / Physic / 7919
School of Physics
  Title:   On Toda Equation and Half BPS Supergravity Solution in M-Theory
  Author(s):  M.A. Ganjali
  Status:   Published
  Journal: JHEP
  Vol.:  01
  Year:  2006
  Pages:   026
  Supported by:  IPM
Recently, it was shown that half BPS Supergravity solution of theories with SU(2|4) 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 PP-wave solution can be written in this fashion.

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