Geodesic
Extended resolvent of the~heat operator with a~multisoliton potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 2, pp. 181-197

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We consider the heat operator with a general multisoliton potential and derive its extended resolvent depending on a parameter $q\in\mathbb{R}^2$. 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.
Keywords: Kadomtsev–Petviashvili equation, heat operator, extended resolvent
Mots-clés : soliton. 
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     author = {M. Boiti and F. Pempinelli and A. K. Pogrebkov},
     title = {Extended resolvent of the~heat operator with a~multisoliton potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {172},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_172_2_a1/}
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M. Boiti; F. Pempinelli; A. K. Pogrebkov. Extended resolvent of the~heat operator with a~multisoliton potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 2, pp. 181-197. http://geodesic.mathdoc.fr/item/TMF_2012_172_2_a1/