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On a formation of singularities of solutions to soliton equations represented by L,A,B-triples Научная публикация

Журнал

Acta Mathematica Sinica, English Series
ISSN: 1439-8516

Вых. Данные

Год: 2024, Том: 40, Номер: 1, Страницы: 406-416 Страниц : 11 DOI: 10.1007/s10114-024-2324-x

Ключевые слова

Soliton equation, blow up, Davey–Stewartson equation, Moutard transformation

Авторы

Taimanov Iskander A. ^1,2

Организации

1	Novosibirsk State University
2	Sobolev Institute of Mathematics

Информация о финансировании (1)

Российский научный фонд

19-11-00044

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.

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

Поступила в редакцию:	27 мая 2022 г.
Принята к публикации:	12 янв. 2023 г.
Опубликована online:	5 янв. 2024 г.
Опубликована в печати:	30 янв. 2024 г.

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

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