Abstract
For an arbitrary perturbation operator, equations for the modulation of the parameters of the KdV soliton are obtained. The asymptotic behavior of the first correction is investigated, and the influence of the leading term of this asymptotic behavior on the soliton phase shift is demonstrated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. P. Novikov (ed.),The Theory of Solitons. The Inverse Scattering Method [in Russian], Nauka, Moscow (1980).
M. J. Ablowitz and H. Segur,Solitons and the Inverse Scattering Transform (SIAM Studies in Applied Maths., Vol. 4), Philadelphia (1981).
A. Newell, in: R. K. Bullough and P. J. Caudrey (eds.),Solitons, Springer, Berlin (1980).
D. J. Kaup,SIAM J. Appl. Math.,31, 121 (1976).
D. J. Kaup and A. S. Newell,Proc. R. Soc. London, Ser. A 361, 413 (1978).
V. I. Karpman and E. M. Maslov,Zh. Eksp. Teor. Fiz.,73, 538 (1977).
J. P. Keener and D. W. Mc-Loughlin,Phys. Rev. A,16, 777 (1977).
D. W. McLaughlin and A. C. Scott,Phys. Rev. A,18, 1652 (1978).
R. L. Sachs,SIAM J. Mat. Anal.,14, 674 (1983).
R. L. Sachs,SIAM J. Mat. Anal.,15, 674 (1984).
R. Grimshaw,Proc. R. Soc. London, Ser. A,368, 359 (1979).
S. A. Vakulenko,Zap. Nauchn. Semin. LOMI,89, 91 (1979).
I. A. Molotov and S. A. Vakulenko,Zap. Nauchn. Semin. LOMI,99, 64 (1980).
A. M. Samsonov,Nonlinear and Turbulent Processes, Vol. 2, No. 4, Harwood Acad. Publ. (1984), p. 1029.
N. N. Bogolyubov and Yu. A. Mitropolsky,Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, New York (1962).
V. P. Maslov,The Complex WKB Method in Nonlinear Equations [in Russian], Nauka, Moscow (1977).
S. Yu. Dobrokhotov and V. P. Maslov,Modern Problems of Mathematics (Reviews of Science and Technology), No. 15 [in Russian], All-Union Institute of Scientific and Technical Information (VINITI), Moscow (1980), p. 3.
I. M. Krichever,Funktsional Analiz i Ego Prilozhen.,22, 37 (1988).
V. P. Maslov and V. A. Tsupin,Dokl. Akad. Nauk SSSR,246, 298 (1979).
V. P. Maslov and G. A. Omel'yanov,Usp. Mat. Nauk,36, 63 (1981).
V. P. Maslov and G. A. Omel'yanov,Sib. Mat. Zh.,24, 172 (1983).
D. J. Kaup,J. Math. Anal. Appl. 54, 849 (1976).
V. S. Gerdzhikov and E. Kh. Khristov,Mat. Zametki,28, 501 (1980).
E. Kh. Khristov,Diff. Uravn.,19, 1548 (1983).
V. A. Arkad'ev, A. K. Pogrebkov, and M. K. Polivanov,Teor. Mat. Fiz.,72, 323 (1987).
M. V. Fedoryuk,The Method of Steepest Descent [in Russian], Nauka, Moscow (1977).
Additional information
Institute of Mathematics at the Computational Center of the Bashkir Scientific Center, Urals Branch, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 92, No. 1, pp. 62–76, July, 1992.
Rights and permissions
About this article
Cite this article
Kalyakin, L.A. Perturbation of the Korteweg-de Vries soliton. Theor Math Phys 92, 736–747 (1992). https://doi.org/10.1007/BF01018701
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01018701