Geodesic
B\"{a}cklund transformations for the one-dimensional Schr\"{o}dinger equation
Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 2, pp. 116-125

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We study the system of equations which bases on the one-dimensional Schrödinger equation and connects the potential, amplitude, and phase functions. Using the methods of compatibility theory of systems of partial differential equations, we obtain the completely integrable systems that connect only two functions of the above three. As a corollary, we construct some exact solutions of the Schrödinger equation.
Keywords: Schrödinger equation, Bäcklund transformation, compatibility condition. 
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     author = {M. V. Neshchadim},
     title = {B\"{a}cklund transformations for the one-dimensional {Schr\"{o}dinger} equation},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
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M. V. Neshchadim. B\"{a}cklund transformations for the one-dimensional Schr\"{o}dinger equation. Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 2, pp. 116-125. http://geodesic.mathdoc.fr/item/SJIM_2021_24_2_a8/