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Reciprocal Bäcklund transformations of autonomous evolution equations. (English. Russian original) Zbl 1179.35265
Theor. Math. Phys. 159, No. 3, 770-778 (2009); translation from Teor. Mat. Fiz. 159, No. 3, 418-427 (2009).
Summary: 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.

MSC:
35Q51 Soliton equations
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
35A30 Geometric theory, characteristics, transformations in context of PDEs
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