Korteweg-de Vries Flows with General Initial Conditions

Name: Korteweg-de Vries Flows with General Initial Conditions
Brand: Springer, Berlin
SKU: 9789819997374
Price: 46767 HUF
Availability: InStock

Szerző: Shinichi Kotani

Nyelv:

Kötés: Kemény kötésű

Kiadó: Springer, Berlin

Elérhetőség: Beszállítói készleten

Küldés 10-13 napon belül

46 767 Ft

Large numbers of studies of the KdV equation have appeared since the pioneering paper by Gardner, Gr...

Információk a könyvről

Szerző

Shinichi Kotani

Nyelv

Angol

Kötés

Könyv - Kemény kötésű

Kiadva

2024

oldal

150

EAN

9789819997374

Enbook ID

44573992

Kiadó

Springer, Berlin

Súly

421

Méretek

155 x 235

Teljes leírás

Large numbers of studies of the KdV equation have appeared since the pioneering paper by Gardner, Greene, Kruskal, and Miura in 1967. Most of those works have employed the inverse spectral method for 1D Schrödinger operators or an advanced Fourier analysis. Although algebraic approaches have been discovered by Hirota-Sato and Marchenko independently, those have not been fully investigated and analyzed. The present book offers a new approach to the study of the KdV equation, which treats decaying initial data and oscillating data in a unified manner. The author's method is to represent the tau functions introduced by Hirota-Sato and developed by Segal-Wilson later in terms of the Weyl-Titchmarsh functions (WT functions, in short) for the underlying Schrödinger operators. The main result is stated by a class of WT functions satisfying some of the asymptotic behavior along a curve approaching the spectrum of the Schrödinger operators at + in an order of -(n-1/2) for the nth KdV equation. This class contains many oscillating potentials (initial data) as well as decaying ones. Especially bounded smooth ergodic potentials are included, and under certain conditions on the potentials, the associated Schrödinger operators have dense point spectrum. This provides a mathematical foundation for the study of the soliton turbulence problem initiated by Zakharov, which was the author's motivation for extending the class of initial data in this book. A large class of almost periodic potentials is also included in these ergodic potentials. P. Deift has conjectured that any solutions to the KdV equation starting from nearly periodic initial data are almost periodic in time. Therefore, our result yields a foundation for this conjecture. For the reader's benefit, the author has included here (1) a basic knowledge of direct and inverse spectral problem for 1D Schrödinger operators, including the notion of the WT functions; (2) Sato's Grassmann manifold method revised by Segal-Wilson; and (3) basic results of ergodic Schrödinger operators.

Érdekelheti

Azok a vásárlók, akik ezt a könyvet megvásárolták, a következőket is megvásárolták

Leggyakrabban keresett

Categories

Authors

Publishers

Termékek

Termékek

Leggyakrabban keresett

Categories

Authors

Publishers

Termékek

Termékek

Korteweg-de Vries Flows with General Initial Conditions

Információk a könyvről

Teljes leírás

Érdekelheti

Azok a vásárlók, akik ezt a könyvet megvásárolták, a következőket is megvásárolták