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Building an extended resolvent of the heat operator via twisting transformations

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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.

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Authors and Affiliations

  1. Dipartimento di Fisica, Università del Salento, Lecce, Italy

    M. Boiti, F. Pempinelli & B. Prinari

  2. INFN, Sezione di Lecce, Lecce, Italy

    M. Boiti, F. Pempinelli & B. Prinari

  3. Steklov Mathematical Institute, RAS, Moscow, Russia

    A. K. Pogrebkov

Authors
  1. M. Boiti
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  2. F. Pempinelli
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  3. A. K. Pogrebkov
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  4. B. Prinari
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Corresponding author

Correspondence to A. K. Pogrebkov.

Additional information

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 159, No. 3, pp. 364–378, June, 2009.

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Boiti, M., Pempinelli, F., Pogrebkov, A.K. et al. Building an extended resolvent of the heat operator via twisting transformations. Theor Math Phys 159, 721–733 (2009). https://doi.org/10.1007/s11232-009-0060-0

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  • DOI: https://doi.org/10.1007/s11232-009-0060-0

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