| Περιγραφή Προγράμματος: | The primary objective of this proposal is to study the generation of rogue waves at a fundamental level. With the implementation of a variety of theories and techniques, from nonlinear physics, nonlinear analysis and dynamical systems, to numerical analysis and simulations, the proposal is expected to achieve progress in the understanding of essential problems in applied mathematics and nonlinear physics. Methodology: we will study the existence of localized nonlinear states, using a variety of techniques (soliton perturbation theory, nonlinear dynamical systems-bifurcation theory and variational methods). We will also study the stability of nonlinear states, by solving equations for perturbations about these states. We will compare stability results between standard NLS models and their extensions. We will study the role and impact of finite boundary conditions on the above models (even in 1D cases the behavior of nonlinear localized structures under periodic boundary conditions is quite different from the infinite domain case).
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