Abstract
We introduce a class of reductions of the two-component KP hierarchy that includes the Hirota–Ohta system hierarchy. The description of the reduced hierarchies is based on the Hirota bilinear identity and an extra bilinear relation characterizing the reduction. We derive the reduction conditions in terms of the Lax operator and higher linear operators of the hierarchy, as well as in terms of the basic two-component KP system of equations.
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Funding
The reported study was funded by the RFBR and NSFC (project No. 21-51-53017).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2022, Vol. 211, pp. 37–47 https://doi.org/10.4213/tmf10243.
Appendix Reductions in terms of the Lax–Sato equations
Here, we briefly describe the the two-component KP hierarchy with times (12) [2] in terms of the Lax–Sato equations and discuss the class of reductions corresponding to bilinear relation (13). In the scalar case, reductions of this type were described in [3].
The Lax–Sato equations define the dynamics of pseudodifferential operators
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Bogdanov, L.V., Xue, L. A class of reductions of the two-component KP hierarchy and the Hirota–Ohta system. Theor Math Phys 211, 473–482 (2022). https://doi.org/10.1134/S0040577922040031
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DOI: https://doi.org/10.1134/S0040577922040031