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The Resource A modern introduction to the mathematical theory of water waves, R.S. Johnson

A modern introduction to the mathematical theory of water waves, R.S. Johnson

Label
A modern introduction to the mathematical theory of water waves
Title
A modern introduction to the mathematical theory of water waves
Statement of responsibility
R.S. Johnson
Creator
Subject
Language
eng
Summary
Beginning with the introduction of the appropriate equations of fluid mechanics, Johnson considers classical problems in linear and non-linear water-wave theory, goes on to look at soliton type equations and closes with an introduction to viscosity
Member of
Cataloging source
DLC
http://library.link/vocab/creatorDate
1944-
http://library.link/vocab/creatorName
Johnson, R. S.
Dewey number
532/.593/0151
Illustrations
illustrations
Index
index present
LC call number
QA927
LC item number
.J65 1997
Literary form
non fiction
Nature of contents
bibliography
Series statement
Cambridge texts in applied mathematics
http://library.link/vocab/subjectName
  • Wave-motion, Theory of
  • Water waves
Label
A modern introduction to the mathematical theory of water waves, R.S. Johnson
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 429-435) and indexes
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Mathematical preliminaries -- The governing equations of fluid mechanics: The equation of mass conservation; The equation of motion: Euler's equation; Vorticity, streamlines and irrotational flow -- The boundary conditions for water waves: The kinematic condition; The dynamic condition; The bottom condition; An integrated mass conservation condition; An energy equation and its integral -- Nondimensionalisation and scaling: Nondimensionalisation; Scaling of the variables; Approximate equations -- Some classical problems in water-wave theory -- Linear problems -- Wave propagation for arbitrary depth and wavelength: Particle paths -- Group velocity and the propagation of energy; Concentric waves on deep water -- Wave propagation over variable depth: Linearised gravity waves of any wave number moving over a constant slope; Edge waves over a constant slope -- Ray theory for a slowly varying environment: Steady, oblique plane waves over variable depth; Ray theory in cylindrical geometry; Steady plane waves on a current -- The ship-wave pattern: Kelvin's theory; Ray theory -- Nonlinear problems -- The Stokes wave -- Nonlinear long waves: The method of characteristics; The hodograph transformation -- Hydraulic jump and bore -- Nonlinear waves on a sloping beach -- The solitary wave: The sech2 solitary wave; Integral relations for the solitary wave -- Weakly nonlinear dispersive waves -- Introduction -- The Korteweg-de Vries family of equations: Korteweg-de Vries (KdV) equation; Two-dimensional Korteweg-de Vries (2D KdV) equation; Concentric Korteweg-de Vries (cKdV) equation; Nearly concentric Korteweg-de Vries (ncKdV) equation; Boussinesq equation; Transformations between these equations; Matching to the near-field -- Completely integrable equations: some results from soliton theory: Solution of the Korteweg-de Vries equation; Soliton theory for other equations; Hirota's bilinear method; Conservation laws -- Waves in a nonuniform environment: Waves over a shear flow; The Burns condition; Ring waves over a shear flow; The Korteweg-de Vries equation for variable depth; Oblique interaction of waves -- Slow modulation of dispersive waves -- The evolution of wave packets: Nonlinear Schrodïnger (NLS) equation; Davey-Stewartson (DS) equations; Matching between the NLS and KdV equations -- NLS and DS equations: some results from soliton theory: Solution of the Nonlinear Schrodïnger equation; Bilinear method for the NLS equation; Bilinear form of the DS equations for long waves; Conservation laws for the NLS and DS equations -- Applications of the NLS and DS equations: Stability of the Stokes wave; Modulation of waves over a shear flow; Modulation of waves over variable depth -- Epilogue -- The governing equations with viscosity -- Application to the propagation of gravity waves: Small amplitude harmonic waves; Attenuation of the solitary wave; Undular bore-model I; Undular bore-model II
Control code
36423414
Dimensions
24 cm
Extent
xiv, 445 pages
Isbn
9780521598323
Isbn Type
(pbk.)
Lccn
97005742
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
Other physical details
illustrations
Label
A modern introduction to the mathematical theory of water waves, R.S. Johnson
Publication
Bibliography note
Includes bibliographical references (pages 429-435) and indexes
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Mathematical preliminaries -- The governing equations of fluid mechanics: The equation of mass conservation; The equation of motion: Euler's equation; Vorticity, streamlines and irrotational flow -- The boundary conditions for water waves: The kinematic condition; The dynamic condition; The bottom condition; An integrated mass conservation condition; An energy equation and its integral -- Nondimensionalisation and scaling: Nondimensionalisation; Scaling of the variables; Approximate equations -- Some classical problems in water-wave theory -- Linear problems -- Wave propagation for arbitrary depth and wavelength: Particle paths -- Group velocity and the propagation of energy; Concentric waves on deep water -- Wave propagation over variable depth: Linearised gravity waves of any wave number moving over a constant slope; Edge waves over a constant slope -- Ray theory for a slowly varying environment: Steady, oblique plane waves over variable depth; Ray theory in cylindrical geometry; Steady plane waves on a current -- The ship-wave pattern: Kelvin's theory; Ray theory -- Nonlinear problems -- The Stokes wave -- Nonlinear long waves: The method of characteristics; The hodograph transformation -- Hydraulic jump and bore -- Nonlinear waves on a sloping beach -- The solitary wave: The sech2 solitary wave; Integral relations for the solitary wave -- Weakly nonlinear dispersive waves -- Introduction -- The Korteweg-de Vries family of equations: Korteweg-de Vries (KdV) equation; Two-dimensional Korteweg-de Vries (2D KdV) equation; Concentric Korteweg-de Vries (cKdV) equation; Nearly concentric Korteweg-de Vries (ncKdV) equation; Boussinesq equation; Transformations between these equations; Matching to the near-field -- Completely integrable equations: some results from soliton theory: Solution of the Korteweg-de Vries equation; Soliton theory for other equations; Hirota's bilinear method; Conservation laws -- Waves in a nonuniform environment: Waves over a shear flow; The Burns condition; Ring waves over a shear flow; The Korteweg-de Vries equation for variable depth; Oblique interaction of waves -- Slow modulation of dispersive waves -- The evolution of wave packets: Nonlinear Schrodïnger (NLS) equation; Davey-Stewartson (DS) equations; Matching between the NLS and KdV equations -- NLS and DS equations: some results from soliton theory: Solution of the Nonlinear Schrodïnger equation; Bilinear method for the NLS equation; Bilinear form of the DS equations for long waves; Conservation laws for the NLS and DS equations -- Applications of the NLS and DS equations: Stability of the Stokes wave; Modulation of waves over a shear flow; Modulation of waves over variable depth -- Epilogue -- The governing equations with viscosity -- Application to the propagation of gravity waves: Small amplitude harmonic waves; Attenuation of the solitary wave; Undular bore-model I; Undular bore-model II
Control code
36423414
Dimensions
24 cm
Extent
xiv, 445 pages
Isbn
9780521598323
Isbn Type
(pbk.)
Lccn
97005742
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
Other physical details
illustrations

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      38.944377 -92.326537
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