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Mathematical Problems in Engineering
Volume 2017, Article ID 5157123, 6 pages
Research Article

Bäcklund Transformations between the KdV Equation and a New Nonlinear Evolution Equation

School of Mathematical Sciences, Yangzhou University, Yangzhou, China

Correspondence should be addressed to Xifang Cao; nc.ude.uzy@oacfx

Received 10 January 2017; Accepted 19 February 2017; Published 2 March 2017

Academic Editor: Alessandro Arsie

Copyright © 2017 Xifang Cao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We first give a Bäcklund transformation from the KdV equation to a new nonlinear evolution equation. We then derive two Bäcklund transformations with two pseudopotentials, one of which is from the KdV equation to the new equation and the other from the new equation to itself. As applications, by applying our Bäcklund transformations to known solutions, we construct some novel solutions to the new equation.