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Full-Text Articles in Physical Sciences and Mathematics
On The (Non)-Integrability Of The Perturbed Kdv Hierarchy With Generic Self-Consistent Sources, Vladimir Gerdjikov, Georgi Grahovski, Rossen Ivanov
On The (Non)-Integrability Of The Perturbed Kdv Hierarchy With Generic Self-Consistent Sources, Vladimir Gerdjikov, Georgi Grahovski, Rossen Ivanov
Conference papers
Non-holonomic deformations of integrable equations of the KdV hierarchy are studied by using the expansions over the so-called "squared solutions" (squared eigenfunctions). Such deformations are equivalent to perturbed models with external (self-consistent) sources. In this regard, the KdV6 equation is viewed as a special perturbation of KdV equation. Applying expansions over the symplectic basis of squared eigenfunctions, the integrability properties of the KdV hierarchy with generic self-consistent sources are analyzed. This allows one to formulate a set of conditions on the perturbation terms that preserve the integrability. The perturbation corrections to the scattering data and to the corresponding action-angle variables …
Nonlinear Behaviour Of Sea Surface Waves Based On Low-Gradient Phase-Only Scattering Effects, Jonathan Blackledge, Eugene Coyle, Derek Kearney
Nonlinear Behaviour Of Sea Surface Waves Based On Low-Gradient Phase-Only Scattering Effects, Jonathan Blackledge, Eugene Coyle, Derek Kearney
Conference papers
Nonlinear sea waves generated by the wind, including freak waves, are considered to be phenomena that can be modelled using the nonlinear (cubic) Schrodinger equation, for example. However, there is a problem with this approach which is that sea surface waves, driven by wind speeds of varying strength, must be considered to be composed of two distinct types, namely, linear waves and nonlinear waves. In this paper, we consider a different approach to modelling ‘nonlinear’ waves that is based on a solution to the linear wave equation under a low-gradient, phase-only condition. This approach is entirely compatible with the fluid …