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Solitons.

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This textbook is an introduction to the theory of solitons and its diverse applications to nonlinear systems that arise in the physical sciences. The authors explain the generation and properties of solitons, introducing the mathematical technique known as the Inverse Scattering Transform. Their aim is to present the essence of inverse scattering clearly, rather than rigorously or completely. Thus, the prerequisites (i.e., partial differential equations, calculus of variations, Fourier integrals, linear waves and Sturm-Liouville theory), and more advanced material is explained in the text with useful references to further reading given at the end of each chapter. Worked examples are frequently used to help the reader follow the various ideas, and the exercises at the end of each chapter not only contain applications but also test understanding. Answers, or hints to the solution, are given at the end of the book. Sections and exercises that contain more difficult material are indicated by asterisks.

Solitons.

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Solitons --- Congresses

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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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In the last decade methods and techniques based on supersymmetry have provided deep insights in quantum chromodynamics and other non-supersymmetric gauge theories at strong coupling. This book summarizes major advances in critical solitons in supersymmetric theories, and their implications for understanding basic dynamical regularities of non-supersymmetric theories. After an extended introduction on the theory of critical solitons, including a historical introduction, the authors focus on three topics: non-Abelian strings and confined monopoles; reducing the level of supersymmetry; and domain walls as D-brane prototypes. They also provide a thorough review of issues at the cutting edge, such as non-Abelian flux tubes. The book presents an extensive summary of the current literature so researchers in this field can understand the background and related issues. First published in 2009, this title has been reissued as an Open Access publication on Cambridge Core.

Nuclear physics. --- Solitons. --- Supersymmetry.