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Effect of the radiation component on soliton motion
Phys. Rev. D 32, 1459 – Published 15 September, 1985
DOI: https://doi.org/10.1103/PhysRevD.32.1459
Abstract
The problem of the soliton motion in the case of a nonzero reflection coefficient is solved exactly within the framework of the inverse scattering method. A general method is given for obtaining the asymptotic expressions of the soliton angle variables. As illustrative examples of our procedure, we consider the Korteweg-de Vries equation and its higher analogs, the nonlinear Schrödinger equation, and the sine-Gordon equation.
References (13)
- L. Martínez Alonso, Phys. Rev. Lett. 54, 499 (1985).
- L. Martínez Alonso, J. Math. Phys. 23, 1518 (1982); ibid. 24, 982 (1983); ibid. 24, 2652 (1983); Phys. Rev. D 30, 2595 (1984).
- M. Göckeler, Z. Phys. C 7, 263 (1981); ibid. 11, 125 (1981); K. Sogo and M. Wadati, Prog. Theor. Phys. 69, 431 (1983).
- V. E. Zakharov, Zh. Eksp. Teor. Fiz. 60, 993 (1971) [Sov. Phys. JETP 33, 538 (1971)]; M. J. Ablowitz and A. C. Newell, J. Math. Phys. 14, 1277 (1973); H. Segur, J. Fluid Mech. 59, 721 (1973); M. J. Ablowitz and H. Segur, Stud. Appl. Math. 66, 159 (1982).
- S. Tanaka, Publ. Res. Inst. Math. Sci. (Kyoto Univ.), 10, 367 (1975).
- S. V. Manakov, Zh. Eksp. Teor. Fiz. 65, 1392 (1973) [Sov. Phys. JETP 38, 693 (1974)].
- V. E. Zakharov and S. V. Manakov, Zh. Eksp. Teor. Fiz. 71, 203 (1976) [Sov. Phys. JETP 44, 106 (1976)]; V. Ju Novoksenov, Dokl. Akad. Nauk SSSR 251, 799 (1980) [Sov. Math. Dokl. 21, 529 (1980)]; A. R. Its, 261, 14 (1981) [ 24, 452 (1981)].
- M. J. Ablowitz and Y. Kodama, Stud. Appl. Math. 66, 159 (1982).
- L. D. Faddeev, Trudy Mat. Inst. Steklov 73, 314 (1964) [Amer. Math. Soc. Transl. 2, 65, 139 (1967)]; P. Deift and E. Trubowitz, Comm. Pure Appl. Math. 32, 121 (1979).
- C. S. Gardner, J. M. Green, M. D. Kruskal and R. Miura, Comm. Pure Appl. Math. 27, 97 (1974).
- L. Martínez Alonso, J. Phys. A 17, 2729 (1984).
- V. E. Zakharov and A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971) [Sov. Phys. JETP 34, 62 (1972)].
- V. E. Zakharov, L. A. Takhtadzhyan and L. D. Fadeev, Dokl. Akad. Nauk. SSSR 219, 1334 (1974) [Sov. Phys. Dokl. 19, 824 (1975)].