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Exact solutions for a Dirac-type equation with N-fold Darboux transformation. (English) Zbl 1464.35284

Summary: Based on matrix spectral problems associated with the real special orthogonal Lie algebra so \((3, \mathbb{R})\), a Dirac-type equation is derived by virtue of the zero-curvature equation. Further, an \(N\)-fold Darboux transformation for the Dirac-type equation is constructed by means of the gauge transformation. Finally, as its application, some exact solutions and their figures are obtained via symbolic computation software (Maple). Correction: The authors were supported by the Nature Science Foundation of China (No. 11701334).

MSC:

35Q51 Soliton equations
35Q41 Time-dependent Schrödinger equations and Dirac equations
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
17B81 Applications of Lie (super)algebras to physics, etc.

Software:

Dirac_Laczos; ATFM; Maple
PDFBibTeX XMLCite
Full Text: DOI

References:

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