On a KP-Type Equation for Dispersive System of Weakly Two-Dimensional Viscous Shallow Water Waves

Shahrdad G. Sajjadi; Tim A. Smith; David L. Ross; Timothy Smith

On a KP-Type Equation for Dispersive System of Weakly Two-Dimensional Viscous Shallow Water Waves

Shahrdad G. Sajjadi, Tim A. Smith, David L. Ross, Timothy Smith

Embry-Riddle Aeronautical University

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

Abstract

By analogy to the Korteweg-de Vries (KdV) equation and its viscous counterpart, the Sajjadi and Smith (SAS) equation, the problem of classical solutions for the Kadomtsev-Petviashvili (KP) equation, for weakly two-dimensional shallow water waves on viscous liquids is considered. The existence and uniqueness, as well as sufficient conditions of solvability, for the nonlinear KP equation is established and discussed.

Original language	American English
Journal	Advances and Applications in Fluid Dynamics
Volume	10
State	Published - Jul 2011

Keywords

SAS equation
visous liquids
shallow water waves
solitons
partial differential equations
KdV equation
KP equation

Disciplines

Applied Mathematics
Ordinary Differential Equations and Applied Dynamics
Partial Differential Equations

Cite this

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title = "On a KP-Type Equation for Dispersive System of Weakly Two-Dimensional Viscous Shallow Water Waves",

abstract = " By analogy to the Korteweg-de Vries (KdV) equation and its viscous counterpart, the Sajjadi and Smith (SAS) equation, the problem of classical solutions for the Kadomtsev-Petviashvili (KP) equation, for weakly two-dimensional shallow water waves on viscous liquids is considered. The existence and uniqueness, as well as sufficient conditions of solvability, for the nonlinear KP equation is established and discussed.",

keywords = "SAS equation, visous liquids, shallow water waves, solitons, partial differential equations, KdV equation, KP equation",

author = "Sajjadi, {Shahrdad G.} and Smith, {Tim A.} and Ross, {David L.} and Timothy Smith",

year = "2011",

month = jul,

language = "American English",

volume = "10",

journal = "Advances and Applications in Fluid Dynamics",

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TY - JOUR

T1 - On a KP-Type Equation for Dispersive System of Weakly Two-Dimensional Viscous Shallow Water Waves

AU - Sajjadi, Shahrdad G.

AU - Smith, Tim A.

AU - Ross, David L.

AU - Smith, Timothy

PY - 2011/7

Y1 - 2011/7

N2 - By analogy to the Korteweg-de Vries (KdV) equation and its viscous counterpart, the Sajjadi and Smith (SAS) equation, the problem of classical solutions for the Kadomtsev-Petviashvili (KP) equation, for weakly two-dimensional shallow water waves on viscous liquids is considered. The existence and uniqueness, as well as sufficient conditions of solvability, for the nonlinear KP equation is established and discussed.

AB - By analogy to the Korteweg-de Vries (KdV) equation and its viscous counterpart, the Sajjadi and Smith (SAS) equation, the problem of classical solutions for the Kadomtsev-Petviashvili (KP) equation, for weakly two-dimensional shallow water waves on viscous liquids is considered. The existence and uniqueness, as well as sufficient conditions of solvability, for the nonlinear KP equation is established and discussed.

KW - SAS equation

KW - visous liquids

KW - shallow water waves

KW - solitons

KW - partial differential equations

KW - KdV equation

KW - KP equation

M3 - Article

VL - 10

JO - Advances and Applications in Fluid Dynamics

JF - Advances and Applications in Fluid Dynamics

ER -