Geodesic
Discrete Crum's theorems and lattice KdV-type equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 2, pp. 187-206

Voir la notice de l'article provenant de la source Math-Net.Ru

We develop Darboux transformations ($DTs$) and their associated Crum's formulas for two Schrödinger-type difference equations that are themselves discretized versions of the spectral problems of the KdV and modified KdV equations. With DTs viewed as a discretization process, classes of semidiscrete and fully discrete KdV-type systems, including the lattice versions of the potential KdV, potential modified KdV, and Schwarzian KdV equations, arise as the consistency condition for the differential/difference spectral problems and their DTs. The integrability of the underlying lattice models, such as Lax pairs, multidimensional consistency, $\tau$-functions, and soliton solutions, can be easily obtained by directly applying the discrete Crum's formulas.
Keywords: discrete Crum's theorem, exact discretization, discrete Schrödinger equation, lattice KdV equations.
Mots-clés : Darboux transformation 
@article{TMF_2020_202_2_a2,
     author = {Cheng Zhang and Linyu Peng and Da-jun Zhang},
     title = {Discrete {Crum's} theorems and lattice {KdV-type} equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {187--206},
     publisher = {mathdoc},
     volume = {202},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_202_2_a2/}
}
TY  - JOUR
AU  - Cheng Zhang
AU  - Linyu Peng
AU  - Da-jun Zhang
TI  - Discrete Crum's theorems and lattice KdV-type equations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2020
SP  - 187
EP  - 206
VL  - 202
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2020_202_2_a2/
LA  - ru
ID  - TMF_2020_202_2_a2
ER  - 
%0 Journal Article
%A Cheng Zhang
%A Linyu Peng
%A Da-jun Zhang
%T Discrete Crum's theorems and lattice KdV-type equations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2020
%P 187-206
%V 202
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2020_202_2_a2/
%G ru
%F TMF_2020_202_2_a2
Cheng Zhang; Linyu Peng; Da-jun Zhang. Discrete Crum's theorems and lattice KdV-type equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 2, pp. 187-206. http://geodesic.mathdoc.fr/item/TMF_2020_202_2_a2/