Cauchy problem for modified Korteweg-de Vries equation with piecewise-type initial data

E. P. Zhidkov; K. P. Kirchev

doi:10.1007/bf00968683

Cauchy problem for modified Korteweg-de Vries equation with piecewise-type initial data

Siberian Mathematical Journal ◽

10.1007/bf00968683 ◽

1985 ◽

Vol 25 (5) ◽

pp. 710-719

Author(s):

E. P. Zhidkov ◽

K. P. Kirchev

Keyword(s):

Cauchy Problem ◽

Initial Data ◽

Vries Equation ◽

De Vries

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On the Cauchy problem for the modified Korteweg-de Vries equation with steplike finite-gap initial data

Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena - Contemporary Mathematics ◽

10.1090/conm/526/10380 ◽

2010 ◽

pp. 151-158 ◽

Cited By ~ 2

Author(s):

Iryna Egorova ◽

Gerald Teschl

Keyword(s):

Cauchy Problem ◽

Initial Data ◽

Vries Equation ◽

De Vries ◽

The Cauchy Problem

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ASYMPTOTICS OF THE SOLUTION OF THE CAUCHY PROBLEM FOR THE KORTEWEG-de VRIES EQUATION WITH INITIAL DATA OF STEP TYPE

Mathematics of the USSR-Sbornik ◽

10.1070/sm1976v028n02abeh001649 ◽

1976 ◽

Vol 28 (2) ◽

pp. 229-248 ◽

Cited By ~ 25

Author(s):

E J Hruslov

Keyword(s):

Cauchy Problem ◽

Initial Data ◽

Vries Equation ◽

De Vries ◽

The Cauchy Problem ◽

Step Type

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The Cauchy Problem for the Korteweg–De Vries Equation with Measures as Initial Data

SIAM Journal on Mathematical Analysis ◽

10.1137/0520041 ◽

1989 ◽

Vol 20 (3) ◽

pp. 582-588 ◽

Cited By ~ 5

Author(s):

Yoshio Tsutsumi

Keyword(s):

Cauchy Problem ◽

Initial Data ◽

Vries Equation ◽

De Vries ◽

The Cauchy Problem

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On the Cauchy problem for the Korteweg–de Vries equation with steplike finite-gap initial data: I. Schwartz-type perturbations

Nonlinearity ◽

10.1088/0951-7715/22/6/009 ◽

2009 ◽

Vol 22 (6) ◽

pp. 1431-1457 ◽

Cited By ~ 23

Author(s):

Iryna Egorova ◽

Katrin Grunert ◽

Gerald Teschl

Keyword(s):

Cauchy Problem ◽

Initial Data ◽

Vries Equation ◽

De Vries ◽

The Cauchy Problem

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ON SOLUTION OF THE CAUCHY PROBLEM FOR THE KORTEWEG-DE VRIES EQUATION WITH INITIAL DATA THE SUM OF A PERIODIC AND A RAPIDLY DECREASING FUNCTION

Mathematics of the USSR-Sbornik ◽

10.1070/sm1989v063n01abeh003272 ◽

1989 ◽

Vol 63 (1) ◽

pp. 257-265 ◽

Cited By ~ 9

Author(s):

N E Firsova

Keyword(s):

Cauchy Problem ◽

Initial Data ◽

Vries Equation ◽

De Vries ◽

The Cauchy Problem

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The Cauchy problem for the Korteweg-de Vries equation when the initial data are irregular

Russian Mathematical Surveys ◽

10.1070/rm1981v036n03abeh004257 ◽

1981 ◽

Vol 36 (3) ◽

pp. 248-249

Author(s):

A V Faminskii

Keyword(s):

Cauchy Problem ◽

Initial Data ◽

Vries Equation ◽

De Vries ◽

The Cauchy Problem

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On the Long-Time Asymptotic Behavior of the Modified Korteweg--de Vries Equation with Step-like Initial Data

SIAM Journal on Mathematical Analysis ◽

10.1137/19m1279964 ◽

2020 ◽

Vol 52 (6) ◽

pp. 5892-5993

Author(s):

Tamara Grava ◽

Alexander Minakov

Keyword(s):

Asymptotic Behavior ◽

Initial Data ◽

Vries Equation ◽

De Vries ◽

Long Time ◽

Time Asymptotic Behavior

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Asymptotic solutions of the Cauchy problem for the singularly perturbed Korteweg-de Vries equation with variable coefficients

Ukrainian Mathematical Journal ◽

10.1007/s11253-007-0008-1 ◽

2007 ◽

Vol 59 (1) ◽

pp. 126-139 ◽

Cited By ~ 4

Author(s):

V. H. Samoilenko ◽

Yu. I. Samoilenko

Keyword(s):

Cauchy Problem ◽

Vries Equation ◽

Variable Coefficients ◽

Singularly Perturbed ◽

Asymptotic Solutions ◽

De Vries ◽

The Cauchy Problem

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Laguerre polynomials and transitional asymptotics of the modified Korteweg–de Vries equation for step-like initial data

Analysis and Mathematical Physics ◽

10.1007/s13324-018-0273-1 ◽

2018 ◽

Vol 9 (4) ◽

pp. 1761-1818 ◽

Cited By ~ 2

Author(s):

M. Bertola ◽

A. Minakov

Keyword(s):

Initial Data ◽

Vries Equation ◽

Laguerre Polynomials ◽

De Vries

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THE LARGE‐TIME DEVELOPMENT OF THE SOLUTION TO AN INITIAL‐VALUE PROBLEM FOR THE KORTEWEG–DE VRIES EQUATION. II. INITIAL DATA HAS A DISCONTINUOUS COMPRESSIVE STEP

Mathematika ◽

10.1112/s0025579313000284 ◽

2014 ◽

Vol 60 (2) ◽

pp. 391-414 ◽

Cited By ~ 5

Author(s):

J. A. Leach ◽

D. J. Needham

Keyword(s):

Initial Data ◽

Initial Value Problem ◽

Large Time ◽

Vries Equation ◽

Time Development ◽

Initial Value ◽

De Vries

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