Semidiscrete Integrable Nonlinear Systems Generated by the New Fourth-Order Spectral Operator: Local Conservation Laws

DOI

10.1142/S1402925111001672How to use a DOI?

Keywords

Zero-curvature equation; fourth-order spectral operator; generating functions; local conservation laws

Abstract

Starting with the semidiscrete integrable nonlinear Schrödinger system on a zigzag-runged ladder lattice we have presented the generalization and an essentially off-diagonal enlargement of its spectral operator which in the framework of zero-curvature equation allows to generate at least two new types of semidiscrete integrable nonlinear systems. The two types of evolutionary operators consistent with the extended spectral operator are proposed. In order to fix arbitrary sampling functions in each type of evolution operators we have to rely upon a restricted collection of lowest local conservation laws whose local densities are independent on the type of admissible evolution operators. For this purpose the modified procedure of seeking the infinite hierarchy of local conservation laws based upon several distinct generating functions has been developed and some lowest local conservation laws have been explicitly obtained.

Copyright

© 2011 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Oleksiy O. Vakhnenko
PY  - 2021
DA  - 2021/01/07
TI  - Semidiscrete Integrable Nonlinear Systems Generated by the New Fourth-Order Spectral Operator: Local Conservation Laws
JO  - Journal of Nonlinear Mathematical Physics
SP  - 401
EP  - 414
VL  - 18
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925111001672
DO  - 10.1142/S1402925111001672
ID  - Vakhnenko2021
ER  -