Quick search Find article
Quick search
Find article

A new approach to the Darboux–Bäcklund transformation versus the standard dressing method

Jan L Cieśliński1 and Waldemar Biernacki2

Show affiliations


We present a new approach to the construction of the Darboux matrix. This is a generalization of a recently formulated method based on the assumption that the square of the Darboux matrix vanishes for some values of the spectral parameter. We consider the multisoliton case, the reduction problem and the discrete case. The relationships between our approach, the Zakharov–Shabat dressing method and the Neugebauer–Meinel method are discussed in detail.


PACS

02.10.Yn Matrix theory

02.30.Jr Partial differential equations

02.40.Hw Classical differential geometry

MSC

37K35 Lie-Bäcklund and other transformations

35Q51 Solitons (See also 37K40)

37K40 Soliton theory, asymptotic behavior of solutions

Subjects

Mathematical physics

Dates

Issue 43 (28 October 2005)

Received 8 June 2005, in final form 19 September 2005

Published 12 October 2005



Related review articles

What's this?
View review articles related to this research to gain an insight into the key trends in this subject area. Related review articles are selected based on PACS/MSC codes, and are no more than three years old.

  1. Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
  2. Trajectory attractors of equations of mathematical physics
  3. Schur function expansions of KP τ-functions associated to algebraic curves

View by subject




Export








Please login to access our web services, or create an account if you don't yet have one.

You must have cookies enabled in your web browser to be able to login.

Username
Password

Forgotten your password? Get a new one here.