Interaction solutions for supersymmetric mKdV-B equation

The ${\cal N} =1$ 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 can be solved by the usual mKdV equation together with a linear differential equations without fermionic variables. 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. An auto-B\"{a}cklund (BT) theorem is obtained by using CTE method. The interaction solutions among solitons and other complicated waves including Painlev\'{e} waves and periodic cnoidal waves are given through an auto-BT theorem. For the soliton-cnoidal interaction solution, two concrete cases are investigated both in analytical and graphical ways by combining the mapping and deformation method.