By Alex Kasman

Solitons are specific suggestions to nonlinear partial differential equations displaying particle-like habit. this is often particularly marvelous, either mathematically and bodily. Waves with those homes have been as soon as believed to be very unlikely by means of best mathematical physicists, but they're no longer merely permitted as a theoretical hazard yet are on a regular basis saw in nature and shape the root of recent fiber-optic communique networks. Glimpses of Soliton conception addresses the various hidden mathematical connections in soliton idea that have been printed over the past half-century. It goals to persuade the reader that, just like the mirrors and hidden wallet utilized by magicians, the underlying algebro-geometric constitution of soliton equations presents a sublime and unusually easy clarification of whatever likely brilliant. Assuming merely multivariable calculus and linear algebra as must haves, this e-book introduces the reader to the KdV Equation and its multisoliton recommendations, elliptic curves and Weierstrass $\wp$-functions, the algebra of differential operators, Lax Pairs and their use in studying different soliton equations, wedge items and decomposability, the KP Equation and Sato's thought concerning the Bilinear KP Equation to the geometry of Grassmannians. extraordinary positive factors of the booklet comprise: cautious number of themes and distinct causes to make this complicated topic obtainable to any undergraduate math significant, a variety of labored examples and thought-provoking yet no longer overly-difficult workouts, footnotes and lists of urged readings to lead the reader to additional information, and use of the software program package deal Mathematica® to facilitate computation and to animate the suggestions lower than examine. This booklet presents the reader with a special glimpse of the team spirit of arithmetic and will shape the root for a self-study, one-semester particular themes, or "capstone" direction.

Show description

Read or Download Glimpses of Soliton Theory: The Algebra and Geometry of Nonlinear Pdes (Student Mathematical Library) PDF

Similar Algebraic Geometry books

Analytic K-Homology (Oxford Mathematical Monographs)

This paintings attracts jointly rules from algebraic topology, practical research and geometry. it's a instrument - a way of conveying details between those 3 matters - and it's been used with luck to find theorems throughout a large span of arithmetic. the aim of this booklet is to acquaint the reader with the fundamental rules of analytic K-homology and increase a few of its functions.

The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra (Graduate Texts in Mathematics)

First textbook-level account of easy examples and strategies during this region. compatible for self-study via a reader who is familiar with a bit commutative algebra and algebraic geometry already. David Eisenbud is a well known mathematician and present president of the yank Mathematical Society, in addition to a profitable Springer writer.

Hilbert

"It provides a delicate portrait of an outstanding person. It describes adequately and intelligibly on a nontechnical point the area of mathematical rules within which Hilbert created his masterpieces. And it illuminates the historical past of German social background opposed to which the drama of Hilberts lifestyles used to be performed.

Introduction to Analysis of the Infinite: Book I

From the preface of the writer: ". .. i've got divided this paintings into books; within the first of those i've got limited myself to these concerns relating natural research. within the moment publication i've got defined these factor which has to be recognized from geometry, when you consider that research is generally constructed in this sort of means that its software to geometry is proven.

Additional resources for Glimpses of Soliton Theory: The Algebra and Geometry of Nonlinear Pdes (Student Mathematical Library)

Show sample text content

Rated 4.03 of 5 – based on 46 votes