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KdV & KAM
This text treats the Korteweg-de Vries (KdV) equation with periodic boundary conditions. This equation models waves in homogeneous, weakly nonlinear and weakly dispersive media in general. For the first time, these important results are comprehensively covered in book form, authored by internationally renowned experts in the field.
Creation of the Sacred
Sacrifice is essential to all religions. Could there be a natural, even biological, reason? Why are sacrifice and numerous other religious rituals and concepts shared by so many different cultures? In this extraordinary book, one of the world’s leading authorities on ancient religions explores the possibility of natural religion.
KdV & KAM
This text treats the Korteweg-de Vries (KdV) equation with periodic boundary conditions. This equation models waves in homogeneous, weakly nonlinear and weakly dispersive media in general. For the first time, these important results are comprehensively covered in book form, authored by internationally renowned experts in the field.
Linear Algebra for the Sciences
This book is based on a course for first-semester science students, held by the second author at the University of Zurich several times. Its goal is threefold: to have students learn a minimal working knowledge of linear algebra, acquire some computational skills, and familiarize them with mathematical language to make mathematical literature more accessible. Therefore, we give precise definitions, introduce helpful notations, and state any results carefully worded. We provide no proofs of these results but typically illustrate them with numerous examples. Additionally, for better understanding, we often give supporting arguments for why they are valid.
KdV & KAM
This text treats the Korteweg-de Vries (KdV) equation with periodic boundary conditions. This equation models waves in homogeneous, weakly nonlinear and weakly dispersive media in general. For the first time, these important results are comprehensively covered in book form, authored by internationally renowned experts in the field.
The Defocusing NLS Equation and Its Normal Form
The theme of this monograph is the nonlinear Schrodinger equation. This equation models slowly varying wave envelopes in dispersive media and arises in various physical systems such as water waves, plasma physics, solid state physics and nonlinear optics. More specifically, this book treats the defocusing nonlinear Schrodinger (dNLS) equation on the circle with a dynamical systems viewpoint. By developing the normal form theory, it is shown that this equation is an integrable partial differential equation in the strongest possible sense. In particular, all solutions of the dNLS equation on the circle are periodic, quasi-periodic or almost-periodic in time and Hamiltonian perturbations of this equation can be studied near solutions far away from the equilibrium. The book is intended not only for specialists working at the intersection of integrable PDEs and dynamical systems but also for researchers farther away from these fields as well as for graduate students. It is written in a modular fashion; each of its chapters and appendices can be read independently of each other.
