Non-truncated formal series symmetries and generalized Virasoro algebra: AKNS-type breaking soliton equation

Abstract

Using the formal series symmetry approach, we obtain three sets of generalized symmetries of the AKNS-type breaking soliton equation. These sets of formal series symmetries are not truncated except that the arbitrary functions of the formal series symmetries are fixed as polynomials of the corresponding independent variables. Differing from the truncated cases such as KP and Toda field equations, these non-truncated symmetries constitute another type of generalization of the Virasoro algebra.