Exact N‐soliton solutions have been obtained for the nonlinear wave equation ∂2w/∂t2 − ∂2w/∂x2 − 6(∂2w2/x2) − ∂4w/∂x4 = 0 which describes motions of long waves in one‐dimensional nonlinear lattices and in shallow‐water under gravity. The solutions have the same functional form as N‐solition solutions of the Korteweg‐de Vries equation.

1.
Ryogo
Hirota
,
Phys. Rev. Lett.
27
,
1192
(
1971
).
2.
Ryogo
Hirota
,
J. Phys. Soc. Jap.
33
,
1456
(
1972
).
3.
Ryogo
Hirota
,
J. Phys. Soc. Jap.
33
,
1459
(
1972
).
4.
Ryogo
Hirota
,
J. Math. Phys.
14
,
000
(
1973
).
5.
N. J. Zabusky, “A synergetic approach to problems of nonlinear dispersive wave propagtion and interaction” in Nonlinear Partial Equations, edited by W. F. Ames (Academic, New York, 1967).
6.
F.
Ursell
,
Proc. Camb. Philos. Soc.
49
,
685
(
1953
).
7.
V. E.
Zakharov
,
Zh. Eksp. Teor.‐Fiz.
60
,
993
(
1971
)
[
V. E.
Zakharov
,
Sov. Phys.‐JETP
33
,
538
(
1971
)].
8.
Miki
Wadati
and
Morikazu
Toda
,
J. Phys. Soc. Jap.
32
,
1403
(
1972
).
9.
M.
Toda
, Proceedings International Conference, Statistical Mechanics, Kyoto 1968,
J. Phys. Soc. Jap. Suppl.
26
,
235
(
1969
).
10.
Ryogo Hirota and Kimio Suzuki, Proc. IEEE, July (1973) (to be published).
11.
Peter D.
Lax
,
Commun. Pure Appl. Math.
21
,
467
(
1968
).
This content is only available via PDF.
You do not currently have access to this content.