Integrable Variants of the Toda Lattice
By introducing bilinear operators of trigonometric type, we propose several novel integrable variants of the famous Toda lattice, two of which can be regarded as integrable discretizations of the Kadomtsev–Petviashvili equation—a universal model describing weakly nonlinear waves in media with disper...
Saved in:
| Published in: | Journal of nonlinear science Vol. 34; no. 5 |
|---|---|
| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
New York
Springer US
01-10-2024
Springer Nature B.V |
| Subjects: | |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | By introducing bilinear operators of trigonometric type, we propose several novel integrable variants of the famous Toda lattice, two of which can be regarded as integrable discretizations of the Kadomtsev–Petviashvili equation—a universal model describing weakly nonlinear waves in media with dispersion of velocity. We also demonstrate that two one-dimensional reductions of these variants can approximate the nonlinear Schrödinger equation and a generalized nonlinear Schrödinger equation well. It turns out that these equations admit meaningful solutions including solitons, breathers, lumps and rogue waves, which are expressed in terms of explicit and closed forms. In particular, it seems to be the first time that rogue wave solutions have been obtained for Toda-type equations. Furthermore,
g
-periodic wave solutions are also produced in terms of Riemann theta function. An approximation solution of the three-periodic wave is successfully carried out by using a deep neural network. The introduction of trigonometric-type bilinear operators is also efficient in generating new variants together with rich properties for some other integrable equations. |
|---|---|
| ISSN: | 0938-8974 1432-1467 |
| DOI: | 10.1007/s00332-024-10072-0 |