Abstract
In this paper, the bosonization of the superfield Gardner equation in the case of multifermionic parameters is presented and novel traveling wave solutions are extracted from the coupled bosonic equations by using the mapping and deformation relations. In the case of two-fermionic-parameter bosonization procedure, we provide a special solution in the form of Jacobian elliptic functions. Meanwhile, we discuss and formally derive traveling wave solutions of N fermionic parameters bosonization procedure. This technique can also be applied to treat the N = 1 supersymmetry KdV and mKdV systems which are obtained in two limiting cases.
Highlights
The supersymmetry (SUSY), applied to treat fermions and bosons in a unified way in elementary particle physics since the concept first arose in 1971 by Ramond, Golfand and Likhtman, has been researched extensively during past four decades [1]-[6]
The bosonization of the superfield Gardner equation in the case of multifermionic parameters is presented and novel traveling wave solutions are extracted from the coupled bosonic equations by using the mapping and deformation relations
The starting point of SUSY is the supersymmetric versions of well known KdV equation first by Kupershmidt in 1984 and later found independently of the work of Manin-Radual on super KP hierarchy [7] [8] [9] [10]
Summary
The supersymmetry (SUSY), applied to treat fermions and bosons in a unified way in elementary particle physics since the concept first arose in 1971 by Ramond, Golfand and Likhtman, has been researched extensively during past four decades [1]-[6]. We write the N = 1 supersymmetric KdV (sKdV) equation accompanied with a fermionic super-variable. The Gardner equation is called the extended KdV equation with the variable-sign cubic non-linear term or the combined KdV and mKdV (KdV-mKdV) equation It is widely used in various branches of physics, such as plasma physics, fluid physics, nonlinear phenomena and quantum field theory, etc., and it describes a variety of wave phenomena in plasma and solid state [16] [17] [18] [19] [20]. Ren et al used this approach in the N = 1 supersymmetric Burgers (SB) system, and the exact solutions of the usual pure bosonic systems are obtained with the mapping and deformation method and Lie point symmetries theory.
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