Titlebook: Direct and Inverse Methods in Nonlinear Evolution Equations; Lectures Given at th Robert M. Conte,Franco Magri,Pavel Winternitz,Anto Book 2

KEGEL

0075-8450 ented by experts in this tutorial book, to find special analytic solutions to both integrable and partially integrable?equations. The direct method to build solutions includes the analysis of singularities à la Painlevé, Lie symmetries leaving the equation invariant, extension of the Hirota method,

熔巖

Sprachen – Sprachmittlung – Integrationsystems such as the Kadomtsev-Petviashvili, two dimensional Toda and Hirota-Miwa equations, the algebraic structure of such nonlinear evolution systems is explained. Finally, extensions of the method including .-analogue, ultra-discrete systems and trilinear forms are also presented.

averse

BRAWL

BIAS

CONE

Exact solutions of nonlinear partial differential equations by singularity analysis,y the same toolbox, when one looks for analytic solutions in closed form. The basic tool is the appropriate use of the singularities of the solutions, and this can be done without knowing these solutions in advance. Since the elaboration of the . by Weiss et al., many improvements have been made. Af

Terminal

Liberate

Nonlinear superposition formulae of integrable partial differential equations by the singular manifclasses of solutions particularly stable under the nonlinear interaction. The existence of such solutions represents one of the different aspects of the property of ., and it can be connected to the existence of a . from which a . can be established.

acclimate

Contend

Lie groups, singularities and solutions of nonlinear partial differential equations, set of differential equations is presented. Special attention is devoted to algorithms for classifying subalgebras of Lie algebras. The concept of conditional symmetries is introduced and applied to perform dimensional reduction.