A Super mKdV Equation: Bosonization, Painlevé Property and Exact Solutions

摘要

The symmetry of the fermionic field is obtained by means of the Lax pair of the mKdV equation.A new super mKdV equation is constructed by virtue of the symmetry of the fermionic form.The super mKdV system is changed to a system of coupled bosonic equations with the bosonization approach.The bosonized SmKdV (BSmKdV) equation admits Painlevé property by the standard singularity analysis.The traveling wave solutions of the BSmKdV system are presented by the mapping and deformation method.We also provide other ideas to construct new super integrable systems.