Bosonization, Painleve property, exact solutions for N=1 supersymmetric mKdV equation
Abstract
The N=1 supersymmetric modified Korteweg-de Vries (SmKdV) system is transformed to a system of coupled bosonic equations with the bosonization approach. The bosonized SmKdV (BSmKdV) passes the Painlev\'{e} test and allows a set of B\"{a}cklund transformation (BT) by truncating the series expansions of the solutions about the singularity manifold. The traveling wave solutions of the BSmKdV system are obtained using the mapping and deformation method. Some special types of exact solutions for the BSmKdV system are found with the solutions and symmetries of the usual mKdV equation. In the meanwhile, the similarity reduction solutions of the system are investigated by using the Lie point symmetry theory. The generalized tanh function expansion method for the BSmKdV system leads to a nonauto-BT theorem. Using the nonauto-BT theorem, the novel exact explicit solutions of the BSmKdV system can be obtained. All these solutions obtained via the bosonization procedure are different from those obtained via other methods.
Keywords
Cite
@article{arxiv.1404.5832,
title = {Bosonization, Painleve property, exact solutions for N=1 supersymmetric mKdV equation},
author = {Bo Ren and Jian-Rong Yang and Ping Liu and Xi-Zhong Liu},
journal= {arXiv preprint arXiv:1404.5832},
year = {2015}
}
Comments
arXiv admin note: add the references in the manuscript