Synopsis
A clear, math‑driven tour of how small dispersion changes the KdV equation’s solutions. This work explains how researchers study the small dispersion limit using the scattering transform and related methods, leading to a weak but revealing description of the solution as dispersion vanishes. The text presents the key ideas and steps without requiring prior deep background, making the concepts approachable for readers with a strong math background.
The book examines how initial data evolve under KdV when a small parameter tends to zero. It traces the path from direct scattering to inverse problems, explains the role of the Riemann–Hilbert framework, and shows how variational conditions determine the limiting behavior. Along the way, it connects historical approaches to modern techniques and clarifies how weak limits arise in this context.
- How the direct and inverse scattering problems are set up for KdV with small dispersion.
- How the Lot of breaking time and weak limits shape the long‑time behavior.
- How variational and Riemann–Hilbert analyses identify the limit and its properties.
- How the results relate to the broader theory of nonlinear waves and dispersive equations.
Ideal for readers of advanced nonlinear PDEs, mathematical physics, and applied analysis who seek a rigorous yet accessible treatment of dispersive limits and their implications for KdV dynamics.
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The Small Dispersion Limit of the Korteweg-Devries Equations (Classic Reprint)
impression à la demandeVendeur : Forgotten Books, London, Royaume-Uni
Évaluation du vendeur 4 sur 5 étoiles
Paperback. Etat : New. Print on Demand. This book delves into the enigmatic world of the Korteweg-de Vries (KdV) equation, a mathematical phenomenon that has enthralled mathematicians and physicists for decades. The KdV equation, initially discovered in the study of shallow water waves, has since found applications in diverse fields such as acoustics, optics, and even quantum physics. The author, a renowned mathematician specializing in the KdV equation, takes the reader on a captivating journey through its history, applications, and the profound insights it has provided into nonlinear wave dynamics. The book masterfully weaves together intricate mathematical concepts with illuminating examples, making the subject accessible to both experts and general readers alike. Beyond its technical brilliance, the book explores the deeper implications of the KdV equation for our understanding of complex systems. The author demonstrates how the KdV equation reveals the underlying order and predictability within seemingly chaotic phenomena, shedding light on the intricate balance between nonlinearity and dispersion. Through this lens, the book offers valuable perspectives on how complex systems evolve and interact in the world around us. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. N° de réf. du vendeur 9781332966967_0
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The Small Dispersion Limit of the KortewegDevries Equations Classic Reprint
Vendeur : PBShop.store US, Wood Dale, IL, Etats-Unis
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PAP. Etat : New. New Book. Shipped from UK. Established seller since 2000. N° de réf. du vendeur LW-9781332966967
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The Small Dispersion Limit of the KortewegDevries Equations Classic Reprint
Vendeur : PBShop.store UK, Fairford, GLOS, Royaume-Uni
Évaluation du vendeur 5 sur 5 étoiles
PAP. Etat : New. New Book. Shipped from UK. Established seller since 2000. N° de réf. du vendeur LW-9781332966967
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EUR 21,95
Expédition à EUR 3,80
Expédition depuis Royaume-Uni vers Etats-Unis
Expédition depuis Royaume-Uni vers Etats-Unis
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