On the integrability of the (1+1)‐dimensional and (2+1)‐dimensional Ito equations

Abstract

Under investigation in this paper are the (1+1)‐dimensional and (2+1)‐dimensional Ito equations. With the help of the Bell polynomials method, Hirota bilinear method and symbolic computation, the bilinear representations, N‐soliton solutions, bilinear Bäcklund transformations and Lax pairs of these two equations are obtained, respectively. In particular, we obtain a new bilinear form and N‐soliton solutions of the (2+1)‐dimensional Ito equation. The bilinear Bäcklund transformation and Lax pair of the (2+1)‐dimensional Ito equation are also obtained for the first time. Copyright © 2014 John Wiley & Sons, Ltd.