Geodesic
Reciprocal B\"acklund transformations of autonomous evolution equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 3, pp. 418-427

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We discuss the construction of reciprocal Bäcklund transformations for evolution equations using integrating factors of zeroth and higher orders with their corresponding conservation laws. As an example, we consider the Harry Dym equation and the Schwarzian KdV equation.
Keywords: nonlinear evolution equation, Bäcklund transformation, conservation law, integrable evolution equation. 
@article{TMF_2009_159_3_a8,
     author = {M. Euler and N. Euler and S. Lundberg},
     title = {Reciprocal {B\"acklund} transformations of autonomous evolution equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {418--427},
     publisher = {mathdoc},
     volume = {159},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_159_3_a8/}
}
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M. Euler; N. Euler; S. Lundberg. Reciprocal B\"acklund transformations of autonomous evolution equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 3, pp. 418-427. http://geodesic.mathdoc.fr/item/TMF_2009_159_3_a8/