Exact solutions of supersymmetric Burgers equation with Bosonization procedure

Abstract

Using bosonization approach, the N D 1 supersymmetric Burgers (SB) system is changed to a system of coupled bosonic equations. The difficulties caused by intractable anticommuting fermionic fields can be effectively avoided with the approach. By solving the coupled bosonic equations, the traveling wave solutions of the SB system can be obtained with the mapping and deformation method. Besides, the richness of the localized excitations of the supersymmetric integrable system is discovered. In the meanwhile, the similarity reduction solutions of the SB system are also studied with the Lie point symmetries theory.

Nonlocal Symmetry Reductions for Bosonized Supersymmetric Burgers Equation

“…The group invariant solutions related to the nonlocal symmetry (8) could not be obtained within the framework of the direct Lie's symmetry method. [28] Based on the symmetry definition, the prolonged systems are invariance under transformations [30] u…”

“…For C 1 = 0, the reduction cases have been studied in Ref. [28]. Because we concentrate on the symmetry reductions related with the nonlocal symmetry (8), two cases, i.e., C 1 ̸ = 0, are considered in detailed.…”

“…It demonstrates that there is a power series solution (27) with the coefficients given by Eq. (28). A solution of the BSB equation ( 4) can be obtained by using the reduction theorem 1.…”

Bosonization Approach and Novel Traveling Wave Solutions of the Superfield Gardner Equation

“…Recently, a simple but powerful bosonization approach, which main idea is to consider fields in a Grassmannian algebra and rewrite a system in a basis of this algebra to arrive at a system of ordinary (commutative) evolution equations, can effectively simplify such systems containing anti-communicating fermionic fields [7] [21] [22]. In [23], B. 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. In [24], the Lie point symmetries of the supersymmetric KdV-a system are considered and similarity reductions of it are conducted.…”