Geodesic
Some integrable nonautonomous dynamical systems with dissipation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 202 (2021), pp. 99-113

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In this paper, we search for new examples of integrable second order, complex, linear, nonautonomous, ordinary differential equations. We use the method of canonical transformations, in which the general solution can be expressed in quadratures by means of an explicit generating function. For some types of equations, we show that the general solution can be constructed as an absolutely and uniformly convergent series of a complex parameter that runs through the whole complex plane, while the real-valued independent variable runs through an arbitrarily large segment of the real axis.
Keywords: nonautonomous dynamical system, integrability, canonical transformation. 
@article{INTO_2021_202_a4,
     author = {M. V. Shamolin},
     title = {Some integrable nonautonomous dynamical systems with dissipation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {99--113},
     publisher = {mathdoc},
     volume = {202},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_202_a4/}
}
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M. V. Shamolin. Some integrable nonautonomous dynamical systems with dissipation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry and Mechanics, Tome 202 (2021), pp. 99-113. http://geodesic.mathdoc.fr/item/INTO_2021_202_a4/