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Solitons --- Particles (Nuclear physics)

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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.

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Solitons. --- Chaotic behavior in systems.

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This thesis by Marcus Kardell presents new contributions to the theory of peaked solitons, focusing on wave equations allowing for a specific type of peaked solitons known as peakons. The work is divided into two papers. The first paper uses Lie symmetry analysis to explore the Novikov and Geng–Xue equations, presenting new peakon-like solutions that exist only for specific time intervals. The second paper examines the interactions between peakons and antipeakons in the Novikov equation, revealing complex dynamics such as periodic solutions and infinite collisions under certain conditions. The thesis aims to enhance the understanding of peakon dynamics and provide valid weak solutions to related equations. It is intended for mathematicians and researchers in wave theory and applied mathematics.

Solitons. --- Wave-motion, Theory of.

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Solitons --- Nonlinear optics --- Evolution equations, Nonlinear