HIROTA BILINEAR FORM FOR THE SUPER-KdV HIERARCHY

Abstract

The integrability of the super-KdV hierarchy suggests that it can be written in Hirota bilinear form as the group orbit equation for some infinite-dimensional Lie algebra. We show how the first few equations in the hierarchy can be written in Hirota bilinear form. We also conjecture a bilinear expression for the whole super-KdV hierarchy and check it to reasonably high orders. A by-product is an expression for the ordinary KdV hierarchy which provides an alternative to the ones obtained by Date et al. and Kac and Wakimoto.

Supersymmetric modified Korteweg–de Vries equation: bilinear approach

“…We will show that above equations (11)(12)(13)(14) imply P 1 = 0 and P 2 = 0. We first work on the case of P 1 .…”

“…This method has been extended to supersymmetric case in [12] [3]. In particular, Carstea, Grammaticos and Ramani constructed the soliton type of solutions for the N = 1 sKdV equation.…”

Bilinear Approach to Supersymmetric KdV Equation

“…We mention that the super-bilinear operator proposed by McArthur and Yung [8] is a particular case of the above super-Hirota operator. We shall note the bilinear operator as…”

Bilinearization and new soliton solutions of Whitham-Broer-Kaup equations with time-dependent coefficients

“…As a direct method, Hirota's bilinear method [15] proposed in 1971 has been widely used to construct multi-soliton solutions of many nonlinear PDEs like those in [5,16,29,32,45,62,63,65]. Besides, Hirota's bilinear method [15] and Darboux transformation [31] are two of the most powerful techniques for constructing rogue-wave solutions [6,28,50] of nonlinear PDEs.…”