URI: http://hdl.handle.net/11122/4608

Date: 2013-08

Type: Thesisms

Table of Contents: Introduction -- Chapter 1. Description of the problem -- Chapter 2. Linearization of the system of shallow water equations -- 2.1. Method of characteristics -- 2.2. Change of variables -- 2.3. Boundary conditions, initial conditions and domain of Φ, the linearized shallow water equation -- 2.4. The limits of applicability of the hodograph transformation -- Chapter 3. Solution of the linearized shallow water equation (the equation (2.19)) -- 3.1. Laplace transformation -- 3.2. Solving the transformed equation -- 3.3. Inverse Laplace transformation -- 3.4. Obtaining the formula for the solution of the linearized shallow water equation -- 3.5. The formula for Φ with a different order of integration -- Chapter 4. Verification of the solution of the linearized equation, obtained by the Laplace transform, for particular cases -- 4.1. Case 1. Plane beach case -- 4.1.1. Method 1. Solving by Laplace transform -- 4.1.2. Method 2. Solving by Fourier-Bessel transform after Carrier-Greenspan -- 4.2. Case 2. An inclined bay with the parabolic cross-section -- 4.2.1. Method 1. Solving by Laplace transform -- 4.2.2. Method 2. Solving by D'Alembert method after Didenkulova and Pelinovsky -- Chapter 5. Relation of the shallow water problem to the wave equation in Rn space -- 5.1. Solution of the wave equation and its spherical mean -- 5.2. Shallow water problems related to the waves in odd-dimensional spaces -- Chapter 6. Sloping bay with the cross-section parameterized by z = cIy ²/₃, c > 0 -- 6.1. Derivation of Φ (λ, σ), the solution of the linearized shallow water equation (6.1) with given initial and boundary conditions -- 6.2. Comparison of the obtained solution Φ for the bay described by z = cIy ²/₃ with the solution obtained through the Laplace transform -- 6.3. Physical characteristics of a wave in the bay and partial derivatives of Φ (λ,σ) -- Chapter 7. Practical experiments -- Conclusion -- References -- Appendix -- Chapter A. Modified Bessel functions and their asymptotic formulas -- A.1. Modified Bessel functions -- A.2. The asymptotic behavior of the modified Bessel functions.