Integrals of Nonlinear Equations of Evolution and Solitary Waves (Classic Reprint)

Integrals of Nonlinear Equations of Evolution and Solitary Waves (Classic Reprint)

by Peter D. Lax
     
 

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Excerpt from Integrals of Nonlinear Equations of Evolution and Solitary Waves

In section 1 we present a general principle for associating nonlinear equations of evolutions with linear operators so that the eigenvalues of the linear operator are integrals of the nonlinear equation. A striking instance of such a procedure is the discovery by Gardner, Miura and Kruskal

Overview

Excerpt from Integrals of Nonlinear Equations of Evolution and Solitary Waves

In section 1 we present a general principle for associating nonlinear equations of evolutions with linear operators so that the eigenvalues of the linear operator are integrals of the nonlinear equation. A striking instance of such a procedure is the discovery by Gardner, Miura and Kruskal that the eigenvalues of the Schrodinger operator are integrals of the Korteweg-de Vries equation.

In section 2 we prove the simplest case of a conjecture of Kruskal and Zabusky concerning the existence of double wave solutions of the Korteweg-de Vries equation, i.e. of solutions which for |t| large behave as the superposition of two solitary waves travelling at different speeds The main tool used is the first of a remarkable series of integrals discovered by Kruskal and Zabusky.

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Product Details

ISBN-13:
9781332144877
Publisher:
FB &c Ltd
Publication date:
08/04/2015
Pages:
62
Product dimensions:
6.00(w) x 9.00(h) x 0.13(d)

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