Algebro‐Geometric Solutions of a (2 + 1)‐Dimensional Integrable Equation Associated with the Ablowitz‐Kaup‐Newell‐Segur Soliton Hierarchy

Xiaohong Chen

Advances in Mathematical Physics, 2022, vol. 2022, issue 1

Abstract: The (2 + 1)‐dimensional Lax integrable equation is decomposed into solvable ordinary differential equations with the help of known (1 + 1)‐dimensional soliton equations associated with the Ablowitz‐Kaup‐Newell‐Segur soliton hierarchy. Then, based on the finite‐order expansion of the Lax matrix, a hyperelliptic Riemann surface and Abel‐Jacobi coordinates are introduced to straighten out the associated flows, from which the algebro‐geometric solutions of the (2 + 1)‐dimensional integrable equation are proposed by means of the Riemann θ functions.

Date: 2022
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https://doi.org/10.1155/2022/4324648

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:4324648

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