Geodesic
KdV equation on a half-line with the zero boundary condition
Teoretičeskaâ i matematičeskaâ fizika, Tome 119 (1999) no. 3, pp. 397-404 Cet article a éte moissonné depuis la source Math-Net.Ru

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We solve the mixed problem for the KdV equation with the boundary condition $u|_{x=0}=0$, $u_{xx}|_{x=0}=0$ using the inverse scattering method. The time evolution of the scattering matrix is efficiently defined from the consistency condition for the spectra of two differential operators giving the $L$–$A$ pair. 
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I. T. Habibullin. KdV equation on a half-line with the zero boundary condition. Teoretičeskaâ i matematičeskaâ fizika, Tome 119 (1999) no. 3, pp. 397-404. http://geodesic.mathdoc.fr/item/TMF_1999_119_3_a3/

[1] V. E. Zakharov, S. V. Manakov, S. P. Novikov, L. P. Pitaevskii, Teoriya solitonov: Metod obratnoi zadachi, Nauka, M., 1980 | MR

[2] J. V. Moloney, A. C. Newell, Phys. Rev. A, 39 (1989), 1809 | DOI

[3] J. Bona, W. G. Pritchard, L. R. Scott, Philos. Trans. R. Soc. London A, 303 (1981), 457 | DOI | MR

[4] J. Bona, R. Winther, SIAM J. Math. Anal., 14 (1983), 1056 | DOI | MR | Zbl

[5] C. K. Chu, R. L. Chou, Adv. Appl. Mech., 27 (1990), 283 | DOI

[6] A. S. Fokas, Physica D, 35 (1989), 167 | DOI | MR | Zbl

[7] A. S. Fokas, A. R. Its, TMF, 92:3 (1992), 387 | MR | Zbl

[8] A. S. Fokas, A. R. Its, SIAM J. Math. Anal., 27:3 (1996), 738 | DOI | MR | Zbl

[9] M. J. Ablowitz, H. J. Segur, J. Math. Phys., 16 (1975), 1054 | DOI | MR | Zbl

[10] E. K. Sklyanin, Funkts. analiz i ego prilozh., 21:2 (1987), 86–87 | MR | Zbl

[11] V. O. Tarasov, Inverse Problems, 7 (1991), 435 | DOI | MR | Zbl

[12] I. T. Khabibullin, TMF, 86:1 (1991), 43 | MR | Zbl

[13] I. T. Habibullin, Phys. Lett. A, 178 (1993), 369 | DOI | MR

[14] B. Gürel, M. Gürses, I. Habibullin, J. Math. Phys., 36:12 (1995), 6809 | DOI | MR | Zbl

[15] V. Adler, B. Gürel, M. Gürses, I. Habibullin, J. Phys. A, 30 (1997), 3505 | DOI | MR | Zbl

[16] V. E. Adler, I. T. Khabibullin, A. B. Shabat, TMF, 110:1 (1997), 98 | DOI | MR | Zbl

[17] M. D. Ramazanov, Matem. sb., 64:2 (1964), 234 ; An Ton Bui, J. Differ. Equ., 25:3 (1977), 288 ; А. В. Фаминский, Труды ММО, 51, 1988, 54 | MR | Zbl | DOI | MR | Zbl

[18] V. A. Marchenko, Operatory Shturma–Liuvillya i ikh prilozheniya, Naukova dumka, Kiev, 1977 | MR

[19] A. B. Shabat, Diff. uravn., 15:10 (1979), 1824 | MR | Zbl

[20] Z. Presdorf, Nekotorye klassy singulyarnykh uravnenii, Mir, M., 1979 | MR