On a KdV Type Equation of Viscous Long Range Water Waves

Shahr Sajjadi; Timothy Smith; Joern Mumme

On a KdV Type Equation of Viscous Long Range Water Waves

Shahr Sajjadi, Timothy Smith, Joern Mumme

Mathematics

Embry-Riddle Aeronautical University

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

Abstract

A generalization of the famous KdV equation is investigated where applications to unidirectional propagation of long water waves on a viscous liquid are considered. The emphasis of this paper is on rigorous mathematical analysis to prove the existence, uniqueness and like properties of the solution of this partial differential equation. In addition, a second generalization equation, KdV with constant coefficients, is considered and like results are provided.

Original language	American English
Journal	Advances and Applications in Fluid Mechanics
Volume	6
State	Published - Jul 2009

Keywords

KdV equation
BBM equation
partial differential equations
water waves
viscous liquid

Disciplines

Partial Differential Equations

Cite this

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title = "On a KdV Type Equation of Viscous Long Range Water Waves",

abstract = " A generalization of the famous KdV equation is investigated where applications to unidirectional propagation of long water waves on a viscous liquid are considered. The emphasis of this paper is on rigorous mathematical analysis to prove the existence, uniqueness and like properties of the solution of this partial differential equation. In addition, a second generalization equation, KdV with constant coefficients, is considered and like results are provided.",

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AU - Smith, Timothy

AU - Mumme, Joern

PY - 2009/7

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N2 - A generalization of the famous KdV equation is investigated where applications to unidirectional propagation of long water waves on a viscous liquid are considered. The emphasis of this paper is on rigorous mathematical analysis to prove the existence, uniqueness and like properties of the solution of this partial differential equation. In addition, a second generalization equation, KdV with constant coefficients, is considered and like results are provided.

AB - A generalization of the famous KdV equation is investigated where applications to unidirectional propagation of long water waves on a viscous liquid are considered. The emphasis of this paper is on rigorous mathematical analysis to prove the existence, uniqueness and like properties of the solution of this partial differential equation. In addition, a second generalization equation, KdV with constant coefficients, is considered and like results are provided.

KW - KdV equation

KW - BBM equation

KW - partial differential equations

KW - water waves

KW - viscous liquid

M3 - Article

VL - 6

JO - Advances and Applications in Fluid Mechanics

JF - Advances and Applications in Fluid Mechanics

ER -