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Full-Text Articles in Physical Sciences and Mathematics
Asymptotic And Numerical Analysis Of Coherent Structures In Nonlinear Schrodinger-Type Equations, Cory Ward
Asymptotic And Numerical Analysis Of Coherent Structures In Nonlinear Schrodinger-Type Equations, Cory Ward
Doctoral Dissertations
This dissertation concerns itself with coherent structures found in nonlinear Schrödinger-type equations and can be roughly split into three parts. In the first part we study a deformation of the defocusing nonlinear Schrödinger (NLS) equation, the defocusing Camassa-Holm NLS (CH-NLS) equation in both one and two space dimensions. We use asymptotic multiscale expansion methods to reduce this model to a Boussinesq-like equation, which is then subsequently used to obtain approximate solitary wave solutions for both the 1D and 2D CH-NLS equations. We then use direct numerical simulations to investigate the validity of these approximate solutions, their evolution, and their head-on …
Riemann-Hilbert Problem, Integrability And Reductions, Vladimir Gerdjikov, Rossen Ivanov, Aleksander Stefanov
Riemann-Hilbert Problem, Integrability And Reductions, Vladimir Gerdjikov, Rossen Ivanov, Aleksander Stefanov
Articles
Abstract. The present paper is dedicated to integrable models with Mikhailov reduction groups GR ≃ Dh. Their Lax representation allows us to prove, that their solution is equivalent to solving Riemann-Hilbert problems, whose contours depend on the realization of the GR-action on the spectral parameter. Two new examples of Nonlinear Evolution Equations (NLEE) with Dh symmetries are presented.
Surface Waves Over Currents And Uneven Bottom, Alan Compelli, Rossen Ivanov, Calin I. Martin, Michail D. Todorov
Surface Waves Over Currents And Uneven Bottom, Alan Compelli, Rossen Ivanov, Calin I. Martin, Michail D. Todorov
Articles
The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom topography is taken into account since it also influences the local wave and current patterns. Specific scaling of the variables is selected which leads to approximations of Boussinesq and KdV types. The arising KdV equation with variable coefficients, dependent on the bottom topography, is studied numerically when the initial condition is in the form of the one soliton solution …
Equatorial Wave–Current Interactions, Adrian Constantin, Rossen Ivanov
Equatorial Wave–Current Interactions, Adrian Constantin, Rossen Ivanov
Articles
We study the nonlinear equations of motion for equatorial wave–current interactions in the physically realistic setting of azimuthal two-dimensional inviscid flows with piecewise constant vorticity in a two-layer fluid with a flat bed and a free surface. We derive a Hamiltonian formulation for the nonlinear governing equations that is adequate for structure-preserving perturbations, at the linear and at the nonlinear level. Linear theory reveals some important features of the dynamics, highlighting differences between the short- and long-wave regimes. The fact that ocean energy is concentrated in the long-wave propagation modes motivates the pursuit of in-depth nonlinear analysis in the long-wave …