In:
Teoreticheskaya i Matematicheskaya Fizika, Steklov Mathematical Institute, Vol. 210, No. 3 ( 2022-3), p. 350-374
Abstract:
By introducing shift relations satisfied by a matrix $\boldsymbol{r}$, we propose a generalized Cauchy matrix scheme and construct a discrete second-order Ablowitz-Kaup-Newell-Segur equation. A modified form of this equation is given. By applying an appropriate skew continuum limit, we obtain the semi-discrete counterparts of these two discrete equations; in the full continuum limit, we derive continuous nonlinear equations. Solutions, including soliton solutions, Jordan-block solutions, and mixed solutions, of the resulting discrete, semi-discrete, and continuous Ablowitz-Kaup-Newell-Segur-type equations are presented. The reductions to discrete, semi-discrete, and continuous nonlinear Schrödinger equations and modified nonlinear Schrödinger equation are also discussed.
Type of Medium:
Online Resource
ISSN:
0564-6162
,
2305-3135
Language:
Russian
Publisher:
Steklov Mathematical Institute
Publication Date:
2022
detail.hit.zdb_id:
2550628-6