Interaction solutions for supersymmetric mKdV-B equation

• The difficulties for fermionic fields are avoided by the bosonization approach.
• The BSmKdV-B equation is proved a CTE solvable system.
• The interaction solutions of the BSmKdV-B system are given with the CTE approach.

The N=1N=1 supersymmetric mKdV-B system is transformed to a system of coupled bosonic equations by using the bosonization approach. The bosonized supersymmetric mKdV-B (BSmKdV-B) equation includes the usual mKdV equation and a linear partial differential equation. The bosonization approach can thus effectively avoid difficulties caused by anticommutative fermionic fields of the supersymmetric systems. The consistent tanh expansion (CTE) method is applied to the BSmKdV-B equation. A nonauto-Bäcklund (BT) theorem is obtained by using CTE method. The interaction solutions among solitons and other complicated waves including Painlevé II waves and periodic cnoidal waves are given through a nonauto-BT theorem. The features of the soliton-cnoidal interaction solutions are investigated both in analytical and graphical ways by combining the mapping and deformation method.