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In this talk, I will review several classes of higher-order generalizations of the integrable Camassa-Holm equation in the Hamiltonian forms. Then, I talk about some new results for one generalized Ca...
In this talk, we investigate the fractalization phenomena for the multi-component systems of the dispersive evolution equations on a bounded interval subject to the periodic boundary conditions. The e...
In this talk, we investigate the revival phenomena for the dispersive evolution equations. Firstly, we study the dispersive quantization phenomena for the multi-component systems of the dispersive evo...
Research on the evolution and function of play at the National Institute for Mathematical and Biological Synthesis (NIMBioS) has culminated in a special issue of the journalAdaptive Behavior. The pape...
We study the evolution of a many-particle system whose wave function obeys the N-body Schr¨ odinger equation under Bose symmetry. The system Hamiltonian describes pairwise particle interactions in the...
The surface of a nanostructure relaxing on a substrate consists of a finite number of interacting steps and often involves the expansion of facets. Prior theoretical studies of facet evolution have fo...
Inspired by the works of Rodnianski and Schlein [31] and Wu [34,35], we derive a new nonlinear Schrödinger equation that describes a second-order correction to the usual tensor product (mean-fiel...
We study the evolution of an N-body weakly interacting system of Bosons. Our work forms an extension of our previous paper Grillakis, Machedon, and Margetis (2010) [13], in which we derived a second-o...
Inspired by the works of Rodnianski and Schlein [31] and Wu [34, 35], we derive a new nonlinear Schr¨odinger equation that describes a second-order correction to the usual tensor product (mean-ʂ...
We study the evolution of a N-body weakly interacting system of Bosons. Our work forms an extension of our previous paper I [13], in which we derived a second-order correction to a mean-field e...
This paper is in part a summary of our earlier work [17, 18, 19], and in part an announcement introducing a re nement of the equations for the pair excitation function used in our previous work with...
An averaging problem with Markov fast motion is considered. The di usive limit is obtained for the evolution of adabatic invariants under the assumption that the averaged motion is ergodic on almost...
We consider the evolution of the separation distance between two particles advected by a random velocity field with slowly decaying temporal and spatial correlations in the weak coupling regime. It ha...
The paper proposes a second-order accurate nite volume local evolution Galerkin (FVLEG) method for two-dimensional special relativistic hydrodynamical (RHD) e-quations. Instead of using the dimensio...
This paper proposes a stochastic model to study the evolution of normal and excess weight population between 24 - 65 years old in the region of Valencia (Spain). An approximate solution process of the...

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