Konno-asai-kakuhata Equation Covariant Prolongation Structure

The prolongation structure theory proposed by Wahlquist and Estabrook is a powerful tool for the analysis of nonlinear integrable equation.Since the prolongation structure equation given by W-E are not manifestly covariant,Guo et al.proposed a covariant prolongation structure theory for the nonlinear evolution equation by means of nonlinear connection theory.The merit of this prolongation structures theory is that it gives the prolongation structures geometry theory.Based upon the covariant prolongation structures theory,we construct the s/(2,R)×R(p) prolongation structure for Konno-Asai-Kakuhata equation in this paper.By taking two and one dimensional prolongation space,we obtain the inverse scattering equations given by Konno et al.and the corresponding Riccati equation.The B(?)cklund transformations are also be presented.