CONNECTIONS OF ZERO CURVATURE AND APPLICATIONS TO NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

被引：2

作者：

Bracken, Paul ^{[1
]}

机构：

[1] Univ Texas, Dept Math, Edinburg, TX 78540 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2014年 / 7卷 / 06期

关键词：

Connection; bundle; curvature; structure equations; lax pair; Backlund; DEFINING REPRESENTATIONS; PROLONGATION STRUCTURES; EVOLUTION; SURFACES; SOLITONS; SYSTEMS;

D O I：

10.3934/dcdss.2014.7.1165

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A general formulation of zero curvature connections in a principle bundle is presented and some applications are discussed. It is proved that a related connection based on a prolongation in an associated bundle remains zero curvature as well. It is also shown that the connection coefficients can be defined so that the partial differential equation to be studied appears as the curvature term in the structure equations. It is discussed how Lax pairs and Backlund tranformations can be formulated for such equations that occur as zero curvature terms.

引用

页码：1165 / 1179

页数：15

共 23 条

[1]

Ablowitz M., 1981, SOLITONS INVERSE SCA, DOI [10.1137/1.9781611970883, DOI 10.1137/1.9781611970883]

[2] NONLINEAR-EVOLUTION EQUATIONS OF PHYSICAL SIGNIFICANCE [J].