Geodesic
Some properties of solutions of a $P$-type nonlinear equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 113 (1997) no. 2, pp. 285-288 
V. V. Tsegel'nik. Some properties of solutions of a $P$-type nonlinear equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 113 (1997) no. 2, pp. 285-288. http://geodesic.mathdoc.fr/item/TMF_1997_113_2_a4/
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     author = {V. V. Tsegel'nik},
     title = {Some properties of solutions of a $P$-type nonlinear equation},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1997_113_2_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

For a nonlinear ordinary differential equation (defining a polinomial Hamiltonian associated with the third Painlev'e equation in the case $\gamma=0$, $\alpha\delta\neq0$) we have obtained Bäcklund transformation and nonlinear functional relationship for solutions corresponding to different values of the parameter of the equation.

[1] V. I. Gromak, N. A. Lukashevich, Analiticheskie svoistva reshenii uravnenii Penleve, Izd-vo “Universitetskoe”, Minsk, 1990 | MR | Zbl

[2] K. Okamoto, Proc. Japan Acad., 56A:8 (1980), 367 | DOI | MR | Zbl

[3] K. Okamoto, Proc. Japan Acad., 56A:6 (1980), 264 | DOI | MR | Zbl

[4] M. Sato, M. Dzimbo, T. Miva, Golonomnye kvantovye polya, Mir, M., 1983

[5] L. Martina, P. Winternitz, Ann. of Phys., 196:2 (1989), 231 | DOI | MR | Zbl

[6] V. I. Gromak, V. V. Tsegelnik, Differents. uravneniya, 30:7 (1994), 1118 | MR | Zbl

[7] V. V. Tsegelnik, TMF, 102:3 (1995), 364 | MR | Zbl