Bosonization, Painleve Property, and Exact Solutions for the N=1 Supersymmetric mKdV Equation

摘要

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 Painleve test and allows a set of Backlund transformations (BTs) by truncating the series expansions. 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. 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 solution of the BSmKdV system can be obtained. All these solutions obtained via the bosonization procedure are different from those obtained via other methods.