Abstract: We discuss the mechanism of formation of singularities of solutions to the Novikov–Veselov, modified Novikov–Veselov, and Davey–Stewartson II (DSII) equations obtained by the Moutard type transformations. These equations admit the L, A, B-triple presentation, the generalization of the L, A-pairs for 2+1-soliton equations. We relate the blow-up of solutions to the non-conservation of the zero level of discrete spectrum of the L-operator. We also present a class of exact solutions, of the DSII system, which depend on two functional parameters, and show that all possible singularities of solutions to DSII equation obtained by the Moutard transformation are indeterminancies, i.e., points when approaching which in different spatial directions the solution has different limits.

Cite: Taimanov I.A.
On a formation of singularities of solutions to soliton equations represented by L,A,B-triples
Acta Mathematica Sinica, English Series. 2024. V.40. N1. P.406-416. DOI: 10.1007/s10114-024-2324-x WOS Scopus РИНЦ OpenAlex

Dates:

Submitted:	May 27, 2022
Accepted:	Jan 12, 2023
Published online:	Jan 5, 2024
Published print:	Jan 30, 2024

Identifiers:

Web of science:	WOS:001136210300006
Scopus:	2-s2.0-85181530848
Elibrary:	65969013
OpenAlex:	W4390599581

Citing: Пока нет цитирований

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