Algebro-geometric solutions of the generalized Burgers hierarchy associated with a 3 × 3 matrix spectral problem based on Riemann surface

Qian Li

Chaos, Solitons & Fractals, 2020, vol. 130, issue C

Abstract: A generalized Burgers hierarchy associated with the 3 × 3 matrix spectral problem is presented with the aid of Lenard recursion equations and the zero-curvature equation. Based on the characteristic polynomial of Lax matrix for the hierarchy, a third order algebraic curve Km−1 with genus m−1 is introduced, on which we establish the associated meromorphic function, Baker–Akhiezer functions and Dubrovin-type equations. Furthermore, the Abel map is introduced to straighten out the corresponding flows. Finally, by employing the property of the meromorphic function and Baker–Akhiezer function and their asymptotic expansions, we derive their explicit Riemann theta function representations. From which algebro-geometric solutions for the whole hierarchy are obtained.

Keywords: Algebro-geometric solutions; The third order algebraic curve; Baker–Akhiezer function; Riemann-theta function (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:130:y:2020:i:c:s0960077919303509

DOI: 10.1016/j.chaos.2019.109409

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