School of Mathematical & Statistical Sciences Faculty Publications

Integrable Peakon Systems

Document Type

Book

Publication Date

8-5-2026

Abstract

This book introduces integrable peaked soliton (peakon) systems, which has been used by mathematical analysists and theoretical physicists to study the Camassa-Holm (CH) equation from various points and extended to create peakon models in nonlinear science. Recently integrable peakon models have been designed that are scalar and vector forms of the peakon systems. Quadratic and cubic peakon models as well as multi-component peakon dynamical systems, new multi-peakon/kink interactions, Hamiltonian systems, Lax pairs, and applications in nonlinear sciences are detailed and explained with examples to aid scientific scholars to conduct theoretical and applied research projects.

Advanced undergraduate and graduate students in applied mathematics, physics and engineering can use this book for a course in integrable peakon systems. The technical aspect of peakon solution will be useful for graduate students and researchers in mathematics, theoretical physics, engineering, nonlinear science and other related fields. Researchers will find the techniques and complicated simulation procedure explored in this book vital for advancing their individual research.

Comments

Introduction - https://rdcu.be/QG9nM9cu9kea

Camassa-Holm (CH) Equation - https://rdcu.be/q7d6z9BnikXa

Degasperis-Procesi (DP) Equation - https://rdcu.be/aBYMuBrRAfRa

Fokas-Olver-Rosenau-Qiao (FORQ) Equation - https://rdcu.be/Mk3tgru6iM5a

Algebro-geometric Solutions and Riemann-Hilbert Problem for the FORQ Hierarchy - https://rdcu.be/yaeRbweszJna

Modified Camassa-Holm (MoCH) Equation -  https://rdcu.be/J9FMf89M8CVa

Global Well-Posedness and Blow-Up for the CH-Type Equations - https://rdcu.be/bddcJTiuyPKa

Two-Component Peakon Systems - https://rdcu.be/UWeJkkQvC1Wa

DOI

10.1007/978-3-032-17779-7

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