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Theoretical and Mathematical Physics

, Volume 159, Issue 3, pp 721–733 | Cite as

Building an extended resolvent of the heat operator via twisting transformations

  • M. Boiti
  • F. Pempinelli
  • A. K. PogrebkovEmail author
  • B. Prinari
Article

Abstract

We introduce twisting transformations for the heat operator. By the simultaneous use of these transformations, N solitons are superimposed à la Darboux on a generic smooth potential decaying at infinity, and the corresponding Jost solutions are generated. We also use these twisting operators to study the existence of the related extended resolvent. We study the existence and uniqueness of the extended resolvent in detail in the case of N solitons with N “incoming” rays and one “outgoing” ray.

Keywords

Darboux transformation multidimensional soliton annihilator 

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Copyright information

© MAIK/Nauka 2009

Authors and Affiliations

  • M. Boiti
    • 1
    • 2
  • F. Pempinelli
    • 1
    • 2
  • A. K. Pogrebkov
    • 3
    Email author
  • B. Prinari
    • 1
    • 2
  1. 1.Dipartimento di FisicaUniversità del SalentoLecceItaly
  2. 2.INFN, Sezione di LecceLecceItaly
  3. 3.Steklov Mathematical InstituteRASMoscowRussia

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