The evolution equations describing the interaction of long and short waves when they are resonantly coupled are discussed. Envelope‐pulse soliton solutions of these equations are constructed using the method of Hirota and the existence of a breather state is shown. The wavetrain modulational characteristics and envelope‐hole solitary wave solutions are also presented.

1.
A.
Hasegawa
,
Phys. Rev. A
1
,
1746
(
1970
).
2.
N.
Yajima
and
M.
Oikawa
,
Progr. Theor. Phys.
56
,
1719
(
1976
).
3.
V. Dj.
Djordjevic
and
L. G.
Redekopp
,
J. Fluid. Mech.
79
,
703
(
1977
).
4.
R. H. J.
Grimshaw
,
Stud. Appl. Math.
56
,
241
(
1977
).
5.
D. J.
Benney
,
Stud. Appl. Math.
55
,
93
(
1976
).
6.
T. B.
Benjamin
and
J. E.
Feir
,
J. Fluid Mech.
27
,
417
(
1967
).
7.
D. J.
Benney
,
Stud. Appl. Math.
56
,
81
(
1977
).
8.
A. C.
Newell
,
SIAM J. Appl. Math.
35
,
650
(
1978
).
9.
R.
Hirota
,
J. Math. Phys.
14
,
805
(
1973
).
10.
Y.‐C.
Ma
,
Stud. Appl. Math.
59
,
201
(
1978
).
11.
V. E.
Zakharov
and
A. B.
Shabat
,
Zh. Eksp. Teor. Fiz.
61
,
118
(
1971
)
[
V. E.
Zakharov
and
A. B.
Shabat
,
Sov. Phys.‐JETP
34
,
61
(
1972
)].
12.
B. M.
Lake
,
H. C.
Yuen
,
H.
Rungaldier
, and
W. E.
Ferguson
,
J. Fluid Mech.
83
,
49
(
1977
).
13.
H. C.
Yuen
and
W. E.
Ferguson
,
Phys. Fluids
21
,
1275
(
1978
).
14.
A.
Hasegawa
and
F. D.
Tappert
,
Appl. Phys. Lett.
23
,
171
(
1973
).
15.
V. E.
Zakharov
and
A. B.
Shabat
,
Zh. Eksp. Teor. Fiz.
64
,
1627
(
1973
)
[
V. E.
Zakharov
and
A. B.
Shabat
,
Sov. Phys.‐JETP
37
,
823
(
1973
)].
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