Structure of Binary Transformations of Darboux Type and Their Application to Soliton Theory

Authors

  • Ya. A. Prykarpatsky
  • A. M. Samoilenko
  • V. G. Samoilenko

Abstract

On the basis of generalized Lagrange identity for pairs of formally adjoint multidimensional differential operators and a special differential geometric structure associated with this identity, we propose a general scheme of the construction of corresponding transformation operators that are described by nontrivial topological characteristics. We construct explicitly the corresponding integro-differential symbols of transformation operators, which are used in the construction of Lax-integrable nonlinear two-dimensional evolutionary equations and their Darboux–Bäcklund-type transformations.

Published

25.12.2003

Issue

Section

Research articles

How to Cite

Prykarpatsky, Ya. A., et al. “Structure of Binary Transformations of Darboux Type and Their Application to Soliton Theory”. Ukrains’kyi Matematychnyi Zhurnal, vol. 55, no. 12, Dec. 2003, pp. 1704-19, https://umj.imath.kiev.ua/index.php/umj/article/view/4032.