Geodesic
Discretization of the~modified Korteweg--de Vries--sine Gordon equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 2, pp. 329-347

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We provide an integrable discretization of the modified Korteweg–de Vries–sine Gordon equation. The discrete form is a coupled system and is derived via the Cauchy matrix approach by introducing suitable discrete plane wave factors. Solutions and a Lax pair are constructed in this approach. The dynamics of some solutions are illustrated. The modified Korteweg–de Vries–sine Gordon equation is recovered in the continuum limit.
Keywords: modified Korteweg–de Vries–sine Gordon equation, Cauchy matrix approach, continuum limit.
Mots-clés : solution, Lax pair 
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     author = {Aye Aye Cho and Jing Wang and Da-jun Zhang},
     title = {Discretization of the~modified {Korteweg--de} {Vries--sine} {Gordon} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {217},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_217_2_a5/}
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Aye Aye Cho; Jing Wang; Da-jun Zhang. Discretization of the~modified Korteweg--de Vries--sine Gordon equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 2, pp. 329-347. http://geodesic.mathdoc.fr/item/TMF_2023_217_2_a5/