Hirota-type Equations, Soliton Solutions, Backlund Transformations and Conservation Laws

Abstract

In this paper, first a class of Hirota-type equations Σ^l_{k=1}H_k(D_x,D_t,D_y)[F_k(D_x,D_t,D_y)f • f] • [G_k(D_x,D_t,D_y)f • f] = 0 are considered. By imposing certain conditions on F_k,G_k and H_k, we show that the abovementioned equation possesses one-soliton solution. Secondly we present a new integrable equation which is an extention of Novikov-Veselov equation and Ito equation. We obtain a Băcklund transformation (BT) of this equation. Finally we consider a generalized equation of Ramani and Sawada-Kotera, and obtain its BT. Starting with the BT an infinite number of conservation laws are derived.