#
A modern introduction to the mathematical theory of water waves, R.S. Johnson
Resource Information
The instance ** A modern introduction to the mathematical theory of water waves, R.S. Johnson** represents a material embodiment of a distinct intellectual or artistic creation found in **University of Missouri Libraries**.

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

The instance

**A modern introduction to the mathematical theory of water waves, R.S. Johnson**represents a material embodiment of a distinct intellectual or artistic creation found in**University of Missouri Libraries**.- Label
- A modern introduction to the mathematical theory of water waves, R.S. Johnson

- Statement of responsibility
- R.S. Johnson

- 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 SchrodÃ¯nger (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 SchrodÃ¯nger 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
- 9780521591720

- Isbn Type
- (hardbound)

- Lccn
- 97005742

- Media category
- unmediated

- Media MARC source
- rdamedia

- Media type code
- n

- Other physical details
- illustrations

- Record ID
- .b3764564x

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