What question did this study set out to answer?

This research explores the relationship between the dual AKP equation and the King-Schief equation, focusing on soliton solutions.

July 9, 2026Mathematical Physics Analysis and Geometry3 citationsOpen Access

On the Relation Between the Dual AKP Equation and an Equation by King and Schief, and its N-soliton Solution

PKPeter H. van der Kamp DZDa‐jun Zhang GQG. Quispel

Key Points

This research explores the relationship between the dual AKP equation and the King-Schief equation, focusing on soliton solutions.
Investigated the equivalence of the dual AKP equation and a 14-point equation linked to the BKP equation.
Showed the duality of the King-Schief equation to Hirota's version of the AKP equation.
Verified the conjectured N-soliton solution through Miwa's parametrization.
Demonstrated the integrability of the dual AKP equation as confirmed by its connection to the King-Schief equation.
Successfully validated the N-soliton solution for the dual AKP equation.
Established a framework linking the soliton solutions of AKP and BKP equations.

Abstract

Abstract The Dual of the lattice AKP (DAKP) equation P.H. van der Kamp et al., J. Phys. A 51, 365202 (2018) is equivalent to a 14-point equation related to the lattice BKP equation, found by King and Schief (KS), and hence it is integrable. We show that the KS equation is dual to Hirota’s version of AKP, and we verify the conjectured N -soliton solution of DAKP, using Miwa’s parametrisation of the AKP and BKP soliton solutions.

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Cite This Study

Kamp et al. (Mon,) studied this question.

synapsesocial.com/papers/6a4f396a2b81a944af574327 https://doi.org/https://doi.org/10.1007/s11040-026-09574-y

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