Variational Bihamiltonian Cohomologies and Integrable Hierarchies III: Linear Reciprocal Transformations

2023/05/18 by Siqi Liu, Zhe Wang, Liu, Si-Qi +3
Physics and Astronomy · Mathematics · Chemistry · #Nonlinear Waves and Solitons #Advanced Differential Equations and Dynamical Systems #Molecular spectroscopy and chirality

paper · pdf · doi:10.48550/arxiv.2305.10851

Abstract

For an integrable hierarchy which possesses a bihamiltonian structure with semisimple hydrodynamic limit, we prove that the linear reciprocal transformation with respect to any of its symmetry transforms it to another bihamiltonian integrable hierarchy. Moreover, we show that the central invariants of the bihamiltonian structure are preserved under such a linear reciprocal transformation.

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