The paper investigates solutions and Lax pairs through bilinear Backlund transformations for some supersymmetric equations. We derive variety of from the known transformations. Besides, using gauge invariance (super) Hirota derivatives we may get deformed consequently with fermionic parameters. Examples are KdV equation KdV1 equation.

Two different types of N = 1 modified KdV equations are shown to possess N soliton solutions. The soliton solutions of these equations are obtained by casting the equations in the bilinear forms using the supersymmetric extension of the Hirota method. The distinguishing features of the soliton solutions of N = 1 mKdV and N = 1 mKdV B equations are discussed. email: [email protected] email: ...

A noncommutative version of the KP equation and two families of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means of Darboux and binary Darboux transformations. Additionally, it is shown that these solutions may also be verified directly. This approach is reminiscent of the wronskian technique used for the Hirota bilinear form of the...

We extend the action for evolution equations of KdV and MKdV type which was derived in NC] to the case of not periodic, but only equivariant phase space variables, introduced in FV2]. The diierence of these variables may be interpreted as reduced phase space variables via a Marsden-Weinstein reduction where the monodromies play the role of the momentum map. As an example we obtain the doubly di...