New Bilinear Bäcklund Transformation and Lax Pair for the Supersymmetric Two‐Boson Equation

Abstract

In this paper, I introduce a class of super Bell polynomials, which are found to play an important role in the characterization of super supersymmetric equations. An effective approach based on the use of the super Bell polynomials is developed to systematically investigate the bilinearization, Bäcklund transformation, and Lax pair for supersymmetric equations. I take a supersymmetric two‐boson equation to illustrate this procedure. A new bilinear Bäcklund transformation and a Lax pair with both fermionic and bosonic parameters are given. In addition, a kind of exact solitons for the equation are further constructed with the help of the bilinear Bäcklund transformation.

Inverse scattering transform for a supersymmetric Korteweg-de Vries equation

“…From the viewpoint of mathematics, supersymmetry originated from theoretical physics is formulated by extending ordinary space to include anticommuting variables of Grassmann type so that bosons and fermions can be treated in a unified way. As the non-commutative extensions of differential systems, supersymmetric equations can model a variety of physical phenomena and dynamical processes [2].…”

Integrability for the generalised variable-coefficient fifth-order Korteweg–de Vries equation with Bell polynomials

“…Many methods such as the Hirota bilinear method [7,8] cannot only be used to find exact solutions [8][9][10], but can also be employed to investigate the integrability of soliton equations [10][11][12][13][14], such as the bilinear Bäcklund transformation (BT) and Lax pair. Recently, the Bell polynomials are linked with the Hirota bilinear method and used to investigate the integrability of soliton equations [15][16][17][18][19][20][21][22][23].…”

The Interactions ofN-Soliton Solutions for the Generalized (2+1)-Dimensional Variable-Coefficient Fifth-Order KdV Equation

“…Especially in the hydromechanics, the nonlinear evolution equations can explain the interaction of the waves by the different dispersion relations. As for the NLEEs, there are many methods to get the solutions, like the Hirota method [8][9][10][11][12][13], the Darboux transformation, Bell-polynomial approach [14][15][16][17][18][19][20], Bäcklund transformations [21,22], and so on [23]. One can get thesoliton solutions and analyze the interactions of the waves based on the Bell-polynomial approach.…”