Ebook: Nonlinear Science Emergence and Dynamics of Coherent Structures

Since Nonlinear Science: Emergence and Dynamics of Coherent Structures went to press in the autumn of 1998, several developments suggest that a second edition would be useful. First have been the experiences of teaching from the book, both by me and by friends and colleagues who have shared their questions and comments, noting typographical errors and suggesting ways in which the material might be better explained or more conveniently arranged. Second, I am now editing the forthcoming Encyclopedia of Nonlinear Science—an activity that corrects misconceptions and provides balanced perspectives on the structure of nonlinear science. Third, I have recently published a survey of neuroscience (Neuroscience: A Mathematical Primer), which motivates revisions of those portions of the present book that are devoted to nerve impulse dynamics. Finally, there have been significant advances in nonlinear science that are appropriate to discuss in a second edition, including new results on the nature of impulse propagation on myelinated nerves, progress in understanding the dynamics of nonlinear lattices (offering appreciations of oscillating self-localized modes or “breathers” and their interactions), and the advent of pump-probe measurements in the infrared range of the electromagnetic spectrum (leading to a spectroscopy of molecular crystals that is sensitive only to nonlinear effects, thereby providing direct indications of self-localization). All of these insights and more have been incorporated into the rewriting of this new edition.

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Since Nonlinear Science: Emergence and Dynamics of Coherent Structures went to press in the autumn of 1998, several developments suggest that a second edition would be useful. First have been the experiences of teaching from the book, both by me and by friends and colleagues who have shared their questions and comments, noting typographical errors and suggesting ways in which the material might be better explained or more conveniently arranged. Second, I am now editing the forthcoming Encyclopedia of Nonlinear Science—an activity that corrects misconceptions and provides balanced perspectives on the structure of nonlinear science. Third, I have recently published a survey of neuroscience (Neuroscience: A Mathematical Primer), which motivates revisions of those portions of the present book that are devoted to nerve impulse dynamics. Finally, there have been significant advances in nonlinear science that are appropriate to discuss in a second edition, including new results on the nature of impulse propagation on myelinated nerves, progress in understanding the dynamics of nonlinear lattices (offering appreciations of oscillating self-localized modes or “breathers” and their interactions), and the advent of pump-probe measurements in the infrared range of the electromagnetic spectrum (leading to a spectroscopy of molecular crystals that is sensitive only to nonlinear effects, thereby providing direct indications of self-localization). All of these insights and more have been incorporated into the rewriting of this new edition.