Geodesic
Local and nonlocal complex discrete sine-Gordon equation. Solutions and continuum limits
Teoretičeskaâ i matematičeskaâ fizika, Tome 211 (2022) no. 3, pp. 375-393

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We study local and nonlocal complex reductions of a discrete negative-order Ablowitz–Kaup–Newell–Segur equation. For the resulting local and nonlocal complex discrete sine-Gordon equations, we construct solutions of the Cauchy matrix type, including soliton solutions and Jordan-block solutions. The dynamics of $1$-soliton solutions are analyzed and illustrated. Continuum limits of the resulting local and nonlocal complex discrete sine-Gordon equations are discussed.
Keywords: local and nonlocal complex discrete sine-Gordon equation, dynamics, continuum limit.
Mots-clés : Cauchy matrix solution 
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     author = {Xiao-bo Xiang and Wei Feng and Song-lin Zhao},
     title = {Local and nonlocal complex discrete {sine-Gordon} equation. {Solutions} and continuum limits},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {375--393},
     publisher = {mathdoc},
     volume = {211},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2022_211_3_a1/}
}
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Xiao-bo Xiang; Wei Feng; Song-lin Zhao. Local and nonlocal complex discrete sine-Gordon equation. Solutions and continuum limits. Teoretičeskaâ i matematičeskaâ fizika, Tome 211 (2022) no. 3, pp. 375-393. http://geodesic.mathdoc.fr/item/TMF_2022_211_3_a1/