Title: The Small Dispersion Limit of the KortewegDevries Equations Classic Reprint
Publisher: Forgotten Books
Publication Date: 2018
Language: English
ISBN 10: 1332966969
ISBN 13: 9781332966967
Binding: PAP
Condition: New
Weight: 245 grams

About this title

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.

About the Author

Peter D. Lax, PhD, is Professor Emeritus of Mathematics at the Courant Institute of Mathematical Sciences at New York University. Dr. Lax is the recipient of the Abel Prize for 2005 "for his groundbreaking contributions to the theory and application of partial differential equations and to the computation of their solutions." * A student and then colleague of Richard Courant, Fritz John, and K. O. Friedrichs, he is considered one of the world's leading mathematicians. He has had a long and distinguished career in pure and applied mathematics, and with over fifty years of experience in the field, he has made significant contributions to various areas of research, including integratable systems, fluid dynamics, and solitonic physics, as well as mathematical and scientific computing.

"About this title" may belong to another edition of this title.

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