Nonlocal conservation laws and related Bäcklund transformations via reciprocal transformations

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.