Geodesic
Revisiting solutions of the Adler–Bobenko–Suris lattice equations and lattice Boussinesq-type equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 3, pp. 474-507 Cet article a éte moissonné depuis la source Math-Net.Ru

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Solutions of all Adler–Bobenko–Suris equations except $Q4$, and of several lattice Boussinesq-type equations are reconsidered by using the Cauchy matrix approach. By introducing a “fake” nonautonomous plane-wave factor, we derive soliton solutions, oscillatory solutions, and semi-oscillatory solutions of the target lattice equations. Unlike the conventional soliton solutions, the oscillatory solutions take constant values on all elementary quadrilaterals on $\mathbb{Z}^2$, which demonstrates a periodic structure.
Keywords: Cauchy matrix approach, Adler–Bobenko–Suris lattice equations, (semi-)oscillatory solutions.
Mots-clés : lattice Boussinesq-type equations, soliton solutions 
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Song-lin Zhao; Kе Yan; Ying-ying Sun. Revisiting solutions of the Adler–Bobenko–Suris lattice equations and lattice Boussinesq-type equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 3, pp. 474-507. http://geodesic.mathdoc.fr/item/TMF_2024_219_3_a4/

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