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Статья

Heat operator with pure soliton potential: properties of the Jost and dual Jost solutions

Journal of Mathematical Physics. 2011. Vol. 52. No. 083506. P. 1-21.
Boiti M., Pempinelli F., Pogrebkov A.
Properties of Jost and dual Jost solutions of the heat equation, F (x,k) and Y(x,k), in the case of a pure solitonic potential are studied in detail.We describe their analytical properties on the spectral parameter k and their asymptotic behavior on the x-plane and we show that the values of e(−qx)F (x, k) and the residues of exp(qx )Y(x,k) at special discrete values of k are bounded functions of x in a polygonal region of the q-plane. Correspondingly, we deduce that the extended version L(q) of the heat operator with a pure solitonic potential has left and right annihilators for q belonging to these polygonal regions.