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A central element in contemporary physics is to understand and describe physical phenomena by employing detailed mathematical models. Frequently, such models lead to large-amplitude or nonlinear systems. Remarkably, in many cases certain prototypical equations are found to be the fundamental underlying systems which can be used to approximate the physical problem.
An important theme in this research is to understand by exact, approximate and numerical methods -- and in close collaboration with state-of-the-art experiments -- solutions to these underlying equations and their properties. Such studies refer to physical problems arising in nonlinear optics, the physics of ultracold atomic gases and Bose-Einstein condensates, nonlinear metamaterials, etc. The main focus is on a special class of solutions, in the form of coherent localized structures, namely solitons in one-dimension and vortex structures in higher-dimensions.
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arXiv (Cornell University)no. 6 (2023)
Social Science Research Network (2022)
arXiv (Cornell University) (2022)
arXiv (Cornell University) (2022)
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