Multidimensional nonlinear integrable systems and methods for constructing their solutions

Vladimir E Zakharov, S. V. Manakov

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

A new method for constructing multidimensional nonlinear integrable systems and their solutions by means of a nonlocal Riemann problem is presented. This is the natural generalization of the method of the local Riemann problem to the case of several space variables and includes the well-known Zakharov-Shabat method of dressing by Volterra operators.

Original languageEnglish (US)
Pages (from-to)3307-3316
Number of pages10
JournalJournal of Soviet Mathematics
Volume31
Issue number6
DOIs
StatePublished - Dec 1985
Externally publishedYes

Fingerprint

Integrable Systems
Nonlinear systems
Nonlinear Systems
Cauchy Problem
Volterra Operator
Nonlocal Problems

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Multidimensional nonlinear integrable systems and methods for constructing their solutions. / Zakharov, Vladimir E; Manakov, S. V.

In: Journal of Soviet Mathematics, Vol. 31, No. 6, 12.1985, p. 3307-3316.

Research output: Contribution to journalArticle

@article{b0300a7a1e6342748c01148e642d8dfc,
title = "Multidimensional nonlinear integrable systems and methods for constructing their solutions",
abstract = "A new method for constructing multidimensional nonlinear integrable systems and their solutions by means of a nonlocal Riemann problem is presented. This is the natural generalization of the method of the local Riemann problem to the case of several space variables and includes the well-known Zakharov-Shabat method of dressing by Volterra operators.",
author = "Zakharov, {Vladimir E} and Manakov, {S. V.}",
year = "1985",
month = "12",
doi = "10.1007/BF02107232",
language = "English (US)",
volume = "31",
pages = "3307--3316",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Science and Business Media Deutschland GmbH",
number = "6",

}

TY - JOUR

T1 - Multidimensional nonlinear integrable systems and methods for constructing their solutions

AU - Zakharov, Vladimir E

AU - Manakov, S. V.

PY - 1985/12

Y1 - 1985/12

N2 - A new method for constructing multidimensional nonlinear integrable systems and their solutions by means of a nonlocal Riemann problem is presented. This is the natural generalization of the method of the local Riemann problem to the case of several space variables and includes the well-known Zakharov-Shabat method of dressing by Volterra operators.

AB - A new method for constructing multidimensional nonlinear integrable systems and their solutions by means of a nonlocal Riemann problem is presented. This is the natural generalization of the method of the local Riemann problem to the case of several space variables and includes the well-known Zakharov-Shabat method of dressing by Volterra operators.

UR - http://www.scopus.com/inward/record.url?scp=0039612716&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039612716&partnerID=8YFLogxK

U2 - 10.1007/BF02107232

DO - 10.1007/BF02107232

M3 - Article

AN - SCOPUS:0039612716

VL - 31

SP - 3307

EP - 3316

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -