On a Formation of Singularities of Solutions to Soliton Equations Represented by L, A, B-triples

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On a Formation of Singularities of Solutions to Soliton Equations Represented by L, A, B-triples. / Taimanov, Iskander A.

In: Acta Mathematica Sinica, English Series, Vol. 40, No. 1, 01.2024, p. 406-416.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{68fc9db912ee44669660fa3756bb0a12,

title = "On a Formation of Singularities of Solutions to Soliton Equations Represented by L, A, B-triples",

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.",

keywords = "35B44, 35Q53, 37K35, 53A10, Davey–Stewartson equation, Moutard transformation, Soliton equation, blow up",

author = "Taimanov, {Iskander A.}",

note = "Supported by RSCF (Grant No. 19-11-00044-P).",

year = "2024",

month = jan,

doi = "10.1007/s10114-024-2324-x",

language = "English",

volume = "40",

pages = "406--416",

journal = "Acta Mathematica Sinica, English Series",

issn = "1439-7617",

publisher = "Springer-Verlag GmbH and Co. KG",

number = "1",

}

RIS

TY - JOUR

T1 - On a Formation of Singularities of Solutions to Soliton Equations Represented by L, A, B-triples

AU - Taimanov, Iskander A.

N1 - Supported by RSCF (Grant No. 19-11-00044-P).

PY - 2024/1

Y1 - 2024/1

N2 - 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.

AB - 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.

KW - 35B44

KW - 35Q53

KW - 37K35

KW - 53A10

KW - Davey–Stewartson equation

KW - Moutard transformation

KW - Soliton equation

KW - blow up

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85181530848&origin=inward&txGid=173900c33b888fa22b126ea279e23d71

UR - https://www.mendeley.com/catalogue/b9108ab8-0038-3cef-8f59-60198b11beb0/

U2 - 10.1007/s10114-024-2324-x

DO - 10.1007/s10114-024-2324-x

M3 - Article

VL - 40

SP - 406

EP - 416

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

SN - 1439-7617

IS - 1

ER -

ID: 60333478