What question did this study set out to answer?

This work aims to integrate the combined AKNS equations using the inverse problem method for a specific operator.

January 22, 2026

Integration of the equation formed by the combination of the equations AKNS(+1) and AKNS(-1) using the inverse problem for periodic Dirac operator

Key Points

This work aims to integrate the combined AKNS equations using the inverse problem method for a specific operator.
Integrated the combined AKNS(+1) and AKNS(-1) equations.
Utilized the inverse problem method for a periodic Dirac operator.
Derived an infinite system of Dubrovin differential equations representing spectral data evolution.
Demonstrated that the Cauchy problem for the Dubrovin system has a unique solution.
Validated findings in the class of continuously differentiable periodic infinite-gap functions.

Abstract

Abstract In this paper, the equation formed by a combination of the equations AKNS ⁡ (+ 1) AKNS (+1) and AKNS ⁡ (- 1) AKNS (-1) was integrated using the inver problem method for the self-adjoint periodic Dirac operator in the class of periodic infinite-gap functions. In addition, an infinite system of Dubrovin differential equations that represents evolution of spectral data of the Dirac operator is derived and it is proved that the Cauchy problem for the system of Dubrovin differential equations has a unique solution in the class of three times continuously differentiable periodic infinite-gap functions.

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Cite This Study

Хасанов et al. (Tue,) studied this question.

synapsesocial.com/papers/6971bdec642b1836717e294a https://doi.org/https://doi.org/10.1515/jiip-2025-0025

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