Geodesic
The limit transition $\mathbb{P}_2\to\mathbb{P}_1$
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 12, Tome 187 (1991), pp. 75-87 
A. A. Kapaev; A. V. Kitaev. The limit transition $\mathbb{P}_2\to\mathbb{P}_1$. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 12, Tome 187 (1991), pp. 75-87. http://geodesic.mathdoc.fr/item/ZNSL_1991_187_a4/
@article{ZNSL_1991_187_a4,
     author = {A. A. Kapaev and A. V. Kitaev},
     title = {The limit transition $\mathbb{P}_2\to\mathbb{P}_1$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {75--87},
     year = {1991},
     volume = {187},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1991_187_a4/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The way which allow to consider the well known limit transition $\mathbb{P}_2\to\mathbb{P}_1$ as a double asymptotic of solutions of equation $\mathbb{P}_2$ in a special “transition” domain which is characterized by the relation $\alpha^2/x^3$, where $\alpha$ is the coefficient of $\mathbb{P}_2$, and $x$ is its argument is found. The importance of Bäcklund transformation for this limit transition is clarified. This limit is studied for all possible solutions of $\mathbb{P}_2$.