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Extended resolvent of the heat operator with a multisoliton potential

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Abstract

We consider the heat operator with a general multisoliton potential and derive its extended resolvent depending on a parameter q ∈ ℝ2. We show that it is bounded in all variables and find its singularities in q. We introduce the Green’s functions and study their properties in detail.

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Authors and Affiliations

  1. Dipartimento di Fisica, Università del Salento and Sezione INFN, Lecce, Italy

    M. Boiti & F. Pempinelli

  2. 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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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. 172, No. 2, pp. 181–197, August, 2012.

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Boiti, M., Pempinelli, F. & Pogrebkov, A.K. Extended resolvent of the heat operator with a multisoliton potential. Theor Math Phys 172, 1037–1051 (2012). https://doi.org/10.1007/s11232-012-0094-6

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  • DOI: https://doi.org/10.1007/s11232-012-0094-6

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