The Small Dispersion Limit of the Korteweg-Devries Equations (Classic Reprint) - Softcover

Inhaltsangabe

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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