Geodesic
Properties of the solitonic potentials of the heat operator
Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 1, pp. 13-23 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study properties of the purely solitonic $\tau$-function and potential of the heat equation in detail. We describe the asymptotic behavior of the potential and establish the ray structure of this asymptotic behavior on the plane $(x_1,x_2)$ in dependence on the parameters of the potential.
Keywords: Kadomtsev–Petviashvili equation, asymptotic potential.
Mots-clés : soliton 
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M. Boiti; F. Pempinelli; A. K. Pogrebkov. Properties of the solitonic potentials of the heat operator. Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 1, pp. 13-23. http://geodesic.mathdoc.fr/item/TMF_2011_168_1_a1/

[1] B. B. Kadomtsev, V. I. Petviashvili, Dokl. AN SSSR, 192 (1970), 753–756 | Zbl

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

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

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

[5] V. D. Lipovskii, Funkts. analiz i ego pril., 20:4 (1986), 35–45 | DOI | MR | Zbl

[6] M. V. Wickerhauser, Comm. Math. Phys., 108:1 (1987), 67–89 | DOI | MR | Zbl

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

[8] M. Boiti, F. Pempinelli, A. K. Pogrebkov, J. Math. Phys., 47:12 (2006), 123510, 43 pp. | DOI | MR | Zbl

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

[10] M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, TMF, 159:3 (2009), 364–378, arXiv: 0901.3857 | 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, TMF, 165:1 (2010), 3–24, arXiv: 0911.1675 | DOI | Zbl

[13] Y. Kodama, J. Phys. A, 43:43 (2010), 434004, 54 pp., arXiv: 1004.4607 | DOI | MR | Zbl

[14] G. Biondini, S. Chakravarty, Math. Comput. Simulation, 74:2–3 (2007), 237–250 | DOI | MR | Zbl

[15] F. R. Gantmakher, Teoriya matrits, Nauka, M., 1988 | MR | Zbl

[16] T. Ando, Linear Algebra Appl., 90 (1987), 165–219 | DOI | MR | Zbl

[17] F. R. Gantmakher, M. G. Krein, Ostsillyatsionnye matritsy i yadra, i malye kolebaniya mekhanicheskikh sistem, GTTI, M., L., 1950 | MR | MR | Zbl

[18] G. Biondini, Y. Kodama, J. Phys. A, 36:42 (2003), 10519–10536, arXiv: nlin/0306003 | DOI | MR | Zbl