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Full-Text Articles in Non-linear Dynamics
One-Dimensional Weakly Nonlinear Model Equations For Rossby Waves, David Henry, Rossen Ivanov
One-Dimensional Weakly Nonlinear Model Equations For Rossby Waves, David Henry, Rossen Ivanov
Articles
In this study we explore several possibilities for modelling weakly nonlinear Rossby waves in fluid of constant depth, which propagate predominantly in one direction. The model equations obtained include the BBM equation, as well as the integrable KdV and Degasperis-Procesi equations.
Integrable Models For Shallow Water With Energy Dependent Spectral Problems, Rossen Ivanov, Tony Lyons
Integrable Models For Shallow Water With Energy Dependent Spectral Problems, Rossen Ivanov, Tony Lyons
Articles
We study the inverse problem for the so-called operators with energy depending potentials. In particular, we study spectral operators with quadratic dependence on the spectral parameter. The corresponding hierarchy of integrable equations includes the Kaup–Boussinesq equation. We formulate the inverse problem as a Riemann–Hilbert problem with a Z2 reduction group. The soliton solutions are explicitly obtained.
Conformal And Geometric Properties Of The Camassa-Holm Hierarchy, Rossen Ivanov
Conformal And Geometric Properties Of The Camassa-Holm Hierarchy, Rossen Ivanov
Articles
Integrable equations with second order Lax pair like KdV and Camassa-Holm (CH) exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants (Schwarz form). These properties for the CH hierarchy are discussed in this ontribution. The squared eigenfunctions of the spectral problem, associated to the Camassa-Holm equation represent a complete basis of functions, which helps to describe the Inverse Scattering Transform (IST) for the Camassa-Holm hierarchy as a Generalised Fourier Transform (GFT). Using GFT we describe explicitly some members of the CH hierarchy, including integrable deformations for the CH equation. Also we show that solutions …