The Discrete Nonlinear Schrodinger Equation Mathematical Analysis, Numerical Computations pdf

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The Discrete Nonlinear Schrodinger Equation Mathematical Analysis, Numerical Computations and Physical Perspectives by Panayotis G. Kevrekidis pdf

The Discrete Nonlinear Schrodinger Equation Mathematical Analysis, Numerical Computations and Physical Perspectives by Panayotis G. Kevrekidis pdf free download. Over the past two decades, the breadth and depth of influence of nonlinear science more generally, and of dispersive lattice systems such as the discrete nonlinear Schr¨odinger (DNLS) equation more specifically, have grown tremendously. Starting from the speculations on Davydov’s soliton in biophysics and nonlinear optical couplers and proposals for waveguide arrays in the 1970s and 1980s, the studies of the DNLS-type systems passed to a different realm in the 1990s through the experimental realization of optical waveguide arrays and the observation of key theoretical predictions including discrete solitons, diffraction, Peierls barriers, multipulse features, and diffraction management.

The Discrete Nonlinear Schrodinger Equation Mathematical Analysis, Numerical Computations and Physical Perspectives by Panayotis G. Kevrekidis pdf

They reemerged in yet another entirely different physical incarnation in Bose–Einstein condensates (BECs) in optical lattices in the
2000s, representing one of the most exciting aspects of nonlinear phenomena in this novel state of matter. This was even more remarkable in view of the wide range of attention that BECs garnered due to their realization being awarded the Nobel prize in Physics in 2001 and their being intimately connected to superfluidity and the Nobel Prize in Physics in 2003. In the meantime, additional related aspects arose in some of the earlier settings, including but not limited to, for instance, the realization of periodic media in photorefractive crystals.

The Discrete Nonlinear Schrodinger Equation Mathematical Analysis, Numerical Computations and Physical Perspectives by Panayotis G. Kevrekidis pdf

I first came across DNLS-type equations during my time as a Ph.D. student, and started working on them during my summer visits at the Center for Nonlinear Studies, at LANL, which has always been a guiding center for work around this theme (even since its original inception!). After the end of my dissertation work, the DNLS became an even stronger focal point, among other reasons due to the increasing visibility of the physical realizations of this deceptively simple-looking mathematical model. Over the years, I have had the privilege to work with a wonderfully diverse, and physically, as well as mathematically gifted set of collaborators from whom I learnt a great deal about this topic; however, I have always been surprised by the fact that despite the level of maturity that this field has arrived at, there has not been a more comprehensive publication (i.e., a book) that focuses on this main theme at the interface of nonlinear science, lattice systems, and wave phenomena.

The Discrete Nonlinear Schrodinger Equation Mathematical Analysis, Numerical Computations and Physical Perspectives by Panayotis G. Kevrekidis pdf

It is in that spirit that I decided to dedicate my first sabbatical from UMass in an effort to sum up some of the main axes of the phenomenology of this equation, at least as I view it and as it has been distilled through my own research efforts on the subject over
the years; undoubtedly, this brings a considerable personal flavor. However, in an effort to broaden the scope of the work, as well as to offer some of its most recent developments, I decided to partition the book into two segments.

The Discrete Nonlinear Schrodinger Equation Mathematical Analysis, Numerical Computations and Physical Perspectives by Panayotis G. Kevrekidis pdf

The Discrete Nonlinear Schrodinger Equation Mathematical Analysis, Numerical Computations and Physical Perspectives by Panayotis G. Kevrekidis pdf


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