Passage to the limitp 2→P 1

A method is given allowing one to consider the well known formal passage to the limit P₂→P₁ as the double asymptotics of solutions of the equation P₂ in a special “transition” domain characterized by the ratio α²/x ³, where α is the parameter of P₂ and x is its argument. It is shown that the sequence of iterated Bäcklund transformations of generic solutions of P₂ is described by a generic solution of P₁. The iterations of Bäcklund transformations of solutions of P₂, both rational and separatrix for x→?∞, are studied. Bibliography: 12 titles.