Nearly linear dynamics of nonlinear dispersive waves

M. B. Erdoǧan; N. Tzirakis; V. Zharnitsky

doi:10.1016/j.physd.2011.05.009

Nearly linear dynamics of nonlinear dispersive waves

M. B. Erdoǧan, N. Tzirakis, V. Zharnitsky

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

Abstract

Dispersive averaging effects are used to show that the Kortewegde Vries (KdV) equation with periodic boundary conditions possesses high frequency solutions, which behave nearly linearly. Numerical simulations are presented, which indicate the high accuracy of this approximation. Furthermore, this result is applied to shallow water wave dynamics in the limit of KdV approximation, which is obtained by asymptotic analysis in combination with numerical simulations of KdV.

Original language	English (US)
Pages (from-to)	1325-1333
Number of pages	9
Journal	Physica D: Nonlinear Phenomena
Volume	240
Issue number	17
DOIs	https://doi.org/10.1016/j.physd.2011.05.009
State	Published - Aug 15 2011

Keywords

Dispersive averaging
KdV
Nonlinear dispersive waves

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

Online availability

10.1016/j.physd.2011.05.009

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title = "Nearly linear dynamics of nonlinear dispersive waves",

abstract = "Dispersive averaging effects are used to show that the Kortewegde Vries (KdV) equation with periodic boundary conditions possesses high frequency solutions, which behave nearly linearly. Numerical simulations are presented, which indicate the high accuracy of this approximation. Furthermore, this result is applied to shallow water wave dynamics in the limit of KdV approximation, which is obtained by asymptotic analysis in combination with numerical simulations of KdV.",

keywords = "Dispersive averaging, KdV, Nonlinear dispersive waves",

author = "Erdoǧan, {M. B.} and N. Tzirakis and V. Zharnitsky",

note = "Funding Information: The authors were partially supported by NSF grants DMS-0900865 (B.E.), DMS-0901222 (N.T.), and DMS-0807897 (V.Z.).",

year = "2011",

month = aug,

day = "15",

doi = "10.1016/j.physd.2011.05.009",

language = "English (US)",

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T1 - Nearly linear dynamics of nonlinear dispersive waves

AU - Erdoǧan, M. B.

AU - Tzirakis, N.

AU - Zharnitsky, V.

N1 - Funding Information: The authors were partially supported by NSF grants DMS-0900865 (B.E.), DMS-0901222 (N.T.), and DMS-0807897 (V.Z.).

PY - 2011/8/15

Y1 - 2011/8/15

N2 - Dispersive averaging effects are used to show that the Kortewegde Vries (KdV) equation with periodic boundary conditions possesses high frequency solutions, which behave nearly linearly. Numerical simulations are presented, which indicate the high accuracy of this approximation. Furthermore, this result is applied to shallow water wave dynamics in the limit of KdV approximation, which is obtained by asymptotic analysis in combination with numerical simulations of KdV.

AB - Dispersive averaging effects are used to show that the Kortewegde Vries (KdV) equation with periodic boundary conditions possesses high frequency solutions, which behave nearly linearly. Numerical simulations are presented, which indicate the high accuracy of this approximation. Furthermore, this result is applied to shallow water wave dynamics in the limit of KdV approximation, which is obtained by asymptotic analysis in combination with numerical simulations of KdV.

KW - Dispersive averaging

KW - KdV

KW - Nonlinear dispersive waves

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JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 17

ER -

Nearly linear dynamics of nonlinear dispersive waves

Abstract

Keywords

ASJC Scopus subject areas

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