R. F. Bikbaev, R. A. Sharipov, “Asymptotics at $t\to\infty$ of the solution to the Cauchy problem for the Korteweg–de Vries equation in the class of potentials with finite-gap behavior as $x\to\pm\infty$”, TMF, 78:3 (1989), 345–356; Theoret. and Math. Phys., 78:3 (1989), 244

Teoreticheskaya i Matematicheskaya Fizika

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

TMF:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Teoreticheskaya i Matematicheskaya Fizika, 1989, Volume 78, Number 3, Pages 345–356 (Mi tmf4790)

This article is cited in 32 scientific papers (total in 33 papers)

Asymptotics at

t \to \infty

$t\to\infty$ of the solution to the Cauchy problem for the Korteweg–de Vries equation in the class of potentials with finite-gap behavior as

x \to \pm \infty

$x\to\pm\infty$

R. F. Bikbaev, R. A. Sharipov

Full-text PDF (1123 kB) Citations (33)

References:

PDF

HTML

Abstract: The Cauchy problem for the KdV equation is considered in the class of functions approaching at

x \to \pm \infty

$x\to\pm\infty$ two different finite-gap solutions of this equation which correspond to the same Riemann surface. With the help of the inverse scattering method the large time asymptotics of the Cauchy problem solution is considered.

Received: 29.08.1987

English version:
Theoretical and Mathematical Physics, 1989, Volume 78, Issue 3, Pages 244–252
DOI: https://doi.org/10.1007/BF01017661

Bibliographic databases:

Language: Russian

Citation: R. F. Bikbaev, R. A. Sharipov, “Asymptotics at

t \to \infty

$t\to\infty$ of the solution to the Cauchy problem for the Korteweg–de Vries equation in the class of potentials with finite-gap behavior as

x \to \pm \infty

$x\to\pm\infty$ ”, TMF, 78:3 (1989), 345–356; Theoret. and Math. Phys., 78:3 (1989), 244–252

Citation in format AMSBIB

\Bibitem{BikSha89}

\by R.~F.~Bikbaev, R.~A.~Sharipov

\paper Asymptotics at~$t\to\infty$ of~the solution to~the Cauchy problem for the Korteweg--de~Vries equation in~the class of~potentials with finite-gap behavior as~$x\to\pm\infty$

\jour TMF

\yr 1989

\vol 78

\issue 3

\pages 345--356

\mathnet{http://mi.mathnet.ru/tmf4790}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=996221}

\zmath{https://zbmath.org/?q=an:0694.35145}

\transl

\jour Theoret. and Math. Phys.

\yr 1989

\vol 78

\issue 3

\pages 244--252

\crossref{https://doi.org/10.1007/BF01017661}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1989AU78400004}

Linking options:

https://www.mathnet.ru/eng/tmf4790

https://www.mathnet.ru/eng/tmf/v78/i3/p345

This publication is cited in the following 33 articles:

A. B. Khasanov, T. G. Khasanov, “The Cauchy Problem for the Nonlinear Complex Modified Korteweg-de Vries Equation with Additional Terms in the Class of Periodic Infinite-Gap Functions”, Sib Math J, 65:4 (2024), 846
A. B. Khasanov, T. G. Khasanov, “Zadacha Koshi dlya nelineinogo kompleksnogo modifitsirovannogo uravneniya Kortevega — de Friza (kmKdF) s dopolnitelnymi chlenami v klasse periodicheskikh beskonechnozonnykh funktsii”, Sib. matem. zhurn., 65:4 (2024), 735–759
Thierry Laurens, “Global Well-Posedness for $H^{-1}(\mathbb {R})$ Perturbations of KdV with Exotic Spatial Asymptotics”, Commun. Math. Phys., 397:3 (2023), 1387
Laurens T., “Kdv on An Incoming Tide”, Nonlinearity, 35:1 (2022), 343–387
U. B. Muminov, A. B. Khasanov, “Zadacha Koshi dlya defokusiruyuschego nelineinogo uravneniya Shredingera s nagruzhennym chlenom”, Matem. tr., 25:1 (2022), 102–133
U. B. Muminov, A. B. Khasanov, “The Cauchy Problem for the Defocusing Nonlinear Schrödinger Equation with a Loaded Term”, Sib. Adv. Math., 32:4 (2022), 277
V. Yu. Novokshenov, “Parametric Resonance in Integrable Systems and Averaging on Riemann Surfaces”, J Math Sci, 258:1 (2021), 65
V. Yu. Novokshenov, “Parametricheskii rezonans v integriruemykh sistemakh i usrednenie na rimanovykh poverkhnostyakh”, Differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 163, VINITI RAN, M., 2019, 65–80
Bertola M., Minakov A., “Laguerre Polynomials and Transitional Asymptotics of the Modified Korteweg-de Vries Equation For Step-Like Initial Data”, Anal. Math. Phys., 9:4 (2019), 1761–1818
Rustem R. Aydagulov, Alexander A. Minakov, “Initial-Boundary Value Problem for Stimulated Raman Scattering Model: Solvability of Whitham Type System of Equations Arising in Long-Time Asymptotic Analysis”, SIGMA, 14 (2018), 119, 19 pp.
Barbara Prinari, Francesco Demontis, Sitai Li, Theodoros P. Horikis, “Inverse scattering transform and soliton solutions for square matrix nonlinear Schrödinger equations with non-zero boundary conditions”, Physica D: Nonlinear Phenomena, 368 (2018), 22
I. Egorova, Z. Gladka, G. Teschl, “On the form of dispersive shock waves of the Korteweg–de Vries equation”, Zhurn. matem. fiz., anal., geom., 12:1 (2016), 3–16
Tamara Grava, Lecture Notes in Physics, 926, Rogue and Shock Waves in Nonlinear Dispersive Media, 2016, 309
I. Egorova, Z. Gladka, T. L. Lange, G. Teschl, “Inverse Scattering Theory for Schrödinger Operators with Steplike Potentials”, Zhurn. matem. fiz., anal., geom., 11:2 (2015), 123–158
Kotlyarov V., Minakov A., “Modulated Elliptic Wave and Asymptotic Solitons in a Shock Problem To the Modified Korteweg-de Vries Equation”, J. Phys. A-Math. Theor., 48:30 (2015), 305201
Iryna Egorova, Zoya Gladka, Volodymyr Kotlyarov, Gerald Teschl, “Long-time asymptotics for the Korteweg–de Vries equation with step-like initial data”, Nonlinearity, 26:7 (2013), 1839
Egorova I., Teschl G., “On the Cauchy Problem for the Kortewegde Vries Equation With Steplike Finite-Gap Initial Data II. Perturbations With Finite Moments”, J Anal Math, 115 (2011), 71–101
Egorova, I, “On the Cauchy problem for the Korteweg-de Vries equation with steplike finite-gap initial data: I. Schwartz-type perturbations”, Nonlinearity, 22:6 (2009), 1431
V. Yu. Novokshenov, “Temporal asymptotics for soliton equations in problems with step initial conditions”, J Math Sci, 125:5 (2005), 717
V. Yu. Novokshenov, “Temporal asymptotics for soliton equations in problems with step initial conditions”, J Math Sci, 125:5 (2005), 717

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	580
Full-text PDF :	163
References:	84
First page:	1

Registration to the website

Logotypes