ABUNDANT SYMMETRY STRUCTURES OF THE BREAKING SOLITON EQUATION

The formal series symmetry approach of obtaining symmetries of a highe r-dimensional partial differential equation is treated as an alternati ve way. For a breaking soliton equation which possesses a (1 + 1)-dime nsional-like recursion operator, six sets of generalized symmetries ar e explicitly given. It is known that the truncated formal series symme tries of the KP and Toda equations constitute the generalized W-infini ty algebra. From this paper we find that the generalized W-infinity al gebra can also be realized by means of the nontruncated formal series symmetries.