Abstract
The N=1 supersymmetric mKdVB system is transformed to a coupled bosonic system by using the bosonization approach. By a singularity structure analysis, the bosonized supersymmetric mKdVB (BSmKdVB) equation admits the Painlevé property. Starting from the standard truncated Painlevé method, the nonlocal symmetry for the BSmKdVB equation is obtained. To solve the first Lie’s principle related with the nonlocal symmetry, the nonlocal symmetry is localized to the Lie point symmetry by introducing multiple new fields. Thanks to localization processes, similarity reductions for the prolonged systems are studied by the Lie point symmetry method. The interaction solutions among solitons and other complicated waves including Painlevé II waves and periodic cnoidal waves are given through the reduction theorems. The soliton-cnoidal wave interaction solutions are explicitly given by using the mapping and deformation method. The concrete soliton-cnoidal interaction solutions are displayed both in analytical and graphical ways.
Highlights
Supersymmetric integrability is a promising topic since super-extensions of nonlinear systems have rich phenomenolgy and still not all the methods used in classical integrability are effective in supersymmetric context.[1,2,3,4] To conquer the difficulties caused by the anticommutative fermionic fields, a bosonization approach is proposed to deal with the supersymmetric integrable systems.[5,6]On the other hand, the nonlocal symmetry is found to play an important role in the theory of integrable systems
The N = 1 supersymmetric mKdVB (SmKdVB) system is transformed to a coupled bosonic system by means of the bosonization approach
The nonlocal symmetry of the bosonized supersymmetric mKdVB (BSmKdVB) equation is obtained by the truncated Painlevé analysis
Summary
Supersymmetric integrability is a promising topic since super-extensions of nonlinear systems have rich phenomenolgy and still not all the methods used in classical integrability are effective in supersymmetric context.[1,2,3,4] To conquer the difficulties caused by the anticommutative fermionic fields, a bosonization approach is proposed to deal with the supersymmetric integrable systems.[5,6]. (2) is called as B-supersymmetric mKdV equation since (2a) is independent of the fermionic variable and (2b) is linear in the fermionic field.[11,12] To avoid the difficulties in dealing with the anticommutative fermionic field in (2), the component fields ξ and u are expanded as the following form by introducing additional two fermionic parameters[5,6,13,14] ξ(x,t) = pζ1 + qζ[2],.
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