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/x3, 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.
KeywordsGeneric Solution Formal Passage Double Asymptotics
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