Nonlocal conservation laws and related B\"acklund transformations via reciprocal transformations
Exactly Solvable and Integrable Systems
2014-06-10 v2 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
A set of infinitely many nonlocal conservation laws are revealed for (1+1)-dimensional evolution equations. For some special known integrable systems, say, the KdV and Dym equations, it is found that different nonlocal conservation laws can lead to same new integrable systems via reciprocal transformation. On the other hand, it can be considered as one solution of the new model obtained via reciprocal transformation(s) can be changed to different solutions of the original model. The fact indicates also that two or more different (local and nonlocal) conservation laws can be used to find implicit auto-B\"acklund transformations via reciprocal transformation to other systems.
Keywords
Cite
@article{arxiv.1402.7231,
title = {Nonlocal conservation laws and related B\"acklund transformations via reciprocal transformations},
author = {Sen-Yue Lou},
journal= {arXiv preprint arXiv:1402.7231},
year = {2014}
}
Comments
5 pages