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This dissertation by Marcus Kardell focuses on new developments in the mathematical theory of peaked solitons, particularly in the context of the Camassa-Holm and Novikov equations. The work is divided into two main papers. The first paper introduces a novel type of peakon-like solutions to the Novikov equation, which exhibit temporal peaks and are characterized by the creation and destruction of peaks over time. These solutions are also explored in relation to the Camassa-Holm equation. The second paper investigates the interactions between peakons and antipeakons, particularly their collisions and the resulting dynamics, within the Novikov equation. This research provides explicit formulas for multipeakon solutions and highlights unique asymptotic behaviors, such as clusters of peakons and antipeakons traveling together. Intended for mathematicians and researchers in applied mathematics, this dissertation contributes to the broader understanding of wave theory and soliton dynamics.

Solitons. --- Differential equations. --- Solitons --- Differential equations

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This book describes both the theoretical and experimental aspects of optical soliton generation, soliton properties and the application of optical solitons to all-optical high-bit-rate communications. Only temporal optical solitons in fibres are considered. The intention of the book is to provide an overview of our current understanding of optical soliton properties, introducing the subject for the student and reviewing the most recent research. Each chapter has been written by experts, indeed chapters 1 and 2 have been contributed by the pioneers of theoretical and experimental optical soliton research - Dr A. Hasegawa and Dr L. F. Mollenauer respectively. The book will be of importance to graduate students and researchers in optics, optical engineering and communications science, providing a useful introduction for those who are entering the field. It will provide an up-to-date summary of recent research for the expert, who will also find the references to each chapter extremely valuable.

Solitons. --- Optical fibers.

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This revised and updated second edition of a highly successful book is the only text at this level to embrace a universal approach to three major developments in classical physics; namely nonlinear waves, solitons and chaos. The authors now include new material on biology and laser theory, and go on to discuss important recent developments such as soliton metamorphosis. A comprehensive treatment of basic plasma and fluid configurations and instabilities is followed by a study of the relevant nonlinear structures. Each chapter concludes with a set of problems. This text will be particularly valuable for students taking courses in nonlinear aspects of physics. In general, it will be of value to final year undergraduates and beginning graduate students studying fluid dynamics, plasma physics and applied mathematics.

Solitons. --- Chaotic behavior in systems. --- Nonlinear waves.

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Skyrme model. --- Skyrmions --- Chirality --- Nuclear models --- Solitons --- Magnetic materials. --- Materials

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The author proves nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as xoinfty. He finds that the amplitude of the line soliton converges to that of the line soliton at initial time whereas jumps of the local phase shift of the crest propagate in a finite speed toward y=pminfty. The local amplitude and the phase shift of the crest of the line solitons are described by a system of 1D wave equations with diffraction terms.

Solitons. --- Wave-motion, Theory of. --- Symmetry (Mathematics) --- Representations of algebras.