Geodesic
Building an extended resolvent of the heat operator via twisting transformations
Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 3, pp. 364-378 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Mots-clés : Darboux transformation, multidimensional soliton
Keywords: annihilator. 
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M. Boiti; F. Pempinelli; A. K. Pogrebkov; B. Prinari. Building an extended resolvent of the heat operator via twisting transformations. Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 3, pp. 364-378. http://geodesic.mathdoc.fr/item/TMF_2009_159_3_a3/

[1] V. S. Dryuma, Pisma v ZhETF, 19:12 (1974), 753–755

[2] V. E. Zakharov, A. B. Shabat, Funkts. analiz i ego pril., 8:3 (1974), 43–53 | DOI | MR | Zbl

[3] M. J. Ablowitz, D. Bar Yaacov, A. S. Fokas, Stud. Appl. Math., 69:2 (1983), 135–143 | DOI | MR | Zbl

[4] P. G. Grinevich, S. P. Novikov, Funkts. analiz i ego pril., 22:1 (1988), 23–33 | DOI | MR | Zbl

[5] M. Boiti, F. Pempinelli, A. K. Pogrebkov, M. C. Polivanov, Inverse Problems, 8:3 (1992), 331–364 | DOI | MR | Zbl

[6] M. Boiti, F. Pempinelli, A. K. Pogrebkov, M. K. Polivanov, TMF, 93:2 (1992), 181–210 | DOI | MR | Zbl

[7] M. Boiti, F. Pempinelli, A. K. Pogrebkov, J. Math. Phys., 35:9 (1994), 4683–4718 | DOI | MR | Zbl

[8] M. Boiti, F. Pempinelli, A. K. Pogrebkov, Inverse Problems, 13:3 (1997), L7–L10 | DOI | MR | Zbl

[9] M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, TMF, 116:1 (1998), 3–53 | DOI | MR | Zbl

[10] B. Prinari, Inverse Problems, 16:3 (2000), 589–603 | DOI | MR | Zbl

[11] M. Boiti, F. Pempinelli, A. Pogrebkov, B. Prinari, Inverse Problems, 17:4 (2001), 937–957 | DOI | MR | Zbl

[12] M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, J. Math. Phys., 43:2 (2002), 1044–1062 | DOI | MR | Zbl

[13] M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, TMF, 144:2 (2005), 257–276 | DOI | MR | Zbl

[14] M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, “Spektralnaya teoriya nestatsionarnogo uravneniya Shrëdingera s dvumerno vozmuschennym odnomernym potentsialom”, Nelineinaya dinamika, Tr. MIAN, 251, ed. E. F. Mischenko, 2005, 10–53 | MR | Zbl

[15] J. Villarroel, M. J. Ablowitz, Stud. Appl. Math., 109:3 (2002), 151–162 | DOI | MR | Zbl

[16] M. Boiti, F. Pempinelli, A. K. Pogrebkov, J. Phys. A, 39:8 (2006), 1877–1898 | DOI | MR | Zbl

[17] M. Boiti, F. Pempinelli, A. K. Pogrebkov, J. Math. Phys., 47:12 (2006), 123510 | DOI | MR | Zbl

[18] S. V. Manakov, V. E. Zakharov, L. A. Bordag, A. R. Its, V. B. Matveev, Phys. Lett. A, 63:3 (1977), 205–206 | DOI | MR

[19] G. Biondini, Y. Kodama, J. Phys. A, 36:42 (2003), 10519–10536 | DOI | MR | Zbl

[20] G. Biondini, S. Chakravarty, J. Math. Phys., 47:3 (2006), 033514 | DOI | MR | Zbl

[21] G. Biondini, Phys. Rev. Lett., 99:6 (2007), 064103 | DOI

[22] S. Chakravarty, Y. Kodama, J. Phys. A, 41:27 (2008), 275209 | DOI | MR | Zbl