Asymptotic approximations for a new eigenvalue in linear problems without a threshold
Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 1, pp. 118-127 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the criterion for a new eigenvalue to appear in the linear spectral problem associated with the intermediate long-wave equation. We compute the asymptotic value of the new eigenvalue in the limit of a small potential using a Fourier decomposition method. We compare the results with those for the Schrödinger operator with a radially symmetrical potential.
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D. E. Pelinovsky; C. Sulem. Asymptotic approximations for a new eigenvalue in linear problems without a threshold. Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 1, pp. 118-127. http://geodesic.mathdoc.fr/item/TMF_2000_122_1_a9/

[1] F. Calogero, A. Degasperis, Spectral Transform and Solitons, North-Holland Publishing Company, Amsterdam, 1982 | MR | Zbl

[2] L. D. Landau, E. M. Lifshits, Kurs teoreticheskoi fiziki. T. 3. Kvantovaya mekhanika. Nerelyativistskaya teoriya, Nauka, M., 1974 | MR

[3] B. Simon, Ann. Phys. (N. Y.), 97 (1976), 279–288 | DOI | MR | Zbl

[4] M. Klaus, B. Simon, Ann. Phys. (N. Y.), 130 (1980), 251–281 | DOI | MR | Zbl

[5] S. M. Apenko, J. Phys. A, 31 (1998), 1553–1562 | DOI | MR | Zbl

[6] Yu. S. Kivshar, D. E. Pelinovsky, T. Cretegny, M. Peyrard, Phys. Rev. Lett., 80 (1998), 5031–5035 | DOI

[7] I. V. Barashenkov, D. E. Pelinovsky, E. V. Zemlyanaya, Phys. Rev. Lett., 80 (1998), 5117–5120 | DOI

[8] D. E. Pelinovsky, C. Sulem, J. Math. Phys., 39 (1998), 6552–6572 | DOI | MR | Zbl

[9] Y. Kodama, M. J. Ablowitz, J. Satsuma, J. Math. Phys., 23 (1982), 564–576 | DOI | MR | Zbl

[10] A. A. Minzoni, T. Miloh, Wave Motion, 20 (1994), 131–142 | DOI | MR | Zbl

[11] I. S. Gradshtein, I. M. Ryzhik, Tablitsy integralov, summ, ryadov i proizvedenii, Fizmatgiz, M., 1971 | MR