J. Phys. Soc. Jpn. 34 (1973) pp. 1289-1296 |Next Article| |Table of Contents|
|Full Text PDF (739K)| |Buy This Article|
The Modified Korteweg-de Vries Equation
Institute for Optical Research, Kyoiku University
(Received November 9, 1972)
It is shown that the Modified Korteweg-de Vries equation can be solved exactly by the “inverse scattering method.” As the special case, the N-soliton solution is obtained explicitly. It is found that N-soliton collision in the Modified Korteweg-de Vries equation is essentially the same as that in the Korteweg-de Vries equation; N-soliton collision is described as the successive collisions of two solitons and there is no effect of multiparticle collisions. Moreover, it is shown that the Modified Korteweg-de Vries equation has new families of the solution.
©1973 The Physical Society of Japan
- N. J. Zabusky: Proc. Symp. Nonlinear Partial Diff. Eqs., ed. W. Ames (Academic Press, 1967).
- T. Kakutani and H. Ono: J. Phys. Soc. Japan 26 (1969) 1305.
- C. S. Gardner, J. M. Greene, M. D. Kruskal and R. M. Miura:
Phys. Rev. Letters 19 (1967) 1095[APS].
- M. Wadati and M. Toda: J. Phys. Soc. Japan 32 (1972) 1403.
- V. E. Zakharov and A. B. Shabat: Soviet Physics JETP 34 (1972) 62.
- P. D. Lax: Comm. Pure appl. Math. 21 (1968) 467.
- M. Wadati: J. Phys. Soc. Japan 32 (1972) 1681.
- S. Tanaka: Proc. Japan Acad. 48 (1972) 466, and preprint.
- L. D. Faddeev: Amer. Math. Soc. Translations Ser. 2 (1968) Vol. 65, p. 139.
- R. Hirota: J. Phys. Soc. Japan 33 (1972) 1456.