In this paper, we investigate the effect of four-wave mixing in the interactions among nonlinear waves such as solitons, breathers, and rogue waves of a coupled generalized nonlinear Schrödinger equation. We explore several interesting results including superposition of breather pulses, increment in the number of breather pulses and in amplitudes of breathers, and rogue waves. By strengthening the four-wave mixing parameter, we observe different transformations that occur between different localized structures. For instance, we visualize a transformation from bright soliton to breather form, bright and dark rogue wave to four-petaled rogue wave structures, four-petaled rogue wave to other rogue wave forms, and so on. Another important observation that we report here is that the interaction of a bright soliton with a rogue wave in the presence of the four-wave mixing effect provides interaction between a dark oscillatory soliton and a rogue wave.

1.
G.
Fibich
,
The Nonlinear Schrödinger Equation: Singular Solutions and Optical Collapse
(
Springer International Publishing
,
2015
).
2.
B. A.
Balomed
, “Nonlinear Schrödinger equation,” in Encyclopedia of Nonlinear Science, edited by A. Scott (Routledge, London, 2005).
3.
S.
Boscolo
and
C.
Finot
,
Shaping Light in Nonlinear Optical Fibers
(
John Wiley & Sons Ltd
,
Chichester
,
2017
).
4.
G. P.
Veldes
,
J.
Borhanian
,
M.
McKerr
,
V.
Saxena
,
D. J.
Fratzeskakis
, and
I.
Kourakis
,
J. Opt.
15
,
064003
(
2013
).
5.
A.
Chabchoub
,
N.
Hoffmann
,
M.
Onorato
, and
N.
Akhmediev
,
Phys. Rev. X
2
,
011015
(
2013
).
6.
J. M.
Dudely
,
F.
Dias
,
M.
Erkintalo
, and
G.
Genty
,
Nat. Photonics
8
,
755
(
2014
).
7.
Y. V.
Bludov
,
V. V.
Konotop
, and
N.
Akhmediev
,
Opt. Lett.
34
,
3015
(
2009
).
8.
K.
Manikandan
,
P.
Muruganandam
,
M.
Senthilvelan
, and
M.
Lakshmanan
,
Phys. Rev. E
90
,
062905
(
2014
).
9.
M.
Onorato
,
S.
Resitori
, and
F.
Baronio
,
Rogue and Shock Waves in Nonlinear Dispersive Media
(
Springer
,
2016
).
10.
D.
Mandelik
,
H. S.
Eisenberg
,
Y.
Silberberg
,
R.
Morandotti
, and
J. S.
Aitchison
,
Phys. Rev. Lett.
90
,
253902
(
2003
).
11.
Y.
Tao
and
J.
He
,
Phys. Rev. E
85
,
026601
(
2012
).
12.
S.
Xu
,
J.
He
, and
L.
Wang
,
Europhys. Lett.
97
,
30007
(
2012
).
13.
14.
Y.
Ohta
and
J.
Yang
,
Phys. Rev. E
86
,
036604
(
2012
).
15.
A.
Ankiewicz
,
J. M.
Sotocrespo
,
M.
Choudhury
, and
N.
Akhmediev
,
J. Opt. Soc. Am. B
30
,
87
(
2013
).
16.
W. X.
Li
,
Z. W.
Guo
,
Z. B.
Guo
, and
Z. H.
Qiang
,
Commun. Theor. Phys.
58
,
531
(
2012
).
17.
X. Y.
Wen
,
Y.
Yang
, and
Z.
Yan
,
Phys. Rev. E
92
,
012917
(
2015
).
18.
X. Y.
Wen
and
D. S.
Wang
,
Wave Motion
79
,
84
(
2018
).
19.
X. Y.
Wen
and
Z.
Yan
,
J. Math. Phys.
59
,
073511
(
2018
).
20.
S. V.
Manakov
,
Sov. Phys. JETP
38
,
248
(
1974
).
21.
C. R.
Menyuk
,
IEEE J. Q. Electron
23
,
174
(
1987
).
22.
Y.
Kodama
and
A. V.
Mikhailov
,
Physica D
152
,
171
(
2001
).
23.
O. C.
Wright
and
M. G.
Forest
,
Physica D
141
,
104
(
2000
).
24.
Q. H.
Park
and
H. J.
Shin
,
IEEE J. Sel. Top. Quantum Electron.
8
,
432
(
2002
).
25.
R.
Radhakrishnan
,
M.
Lakshmanan
, and
J.
Hietarinta
,
Phys. Rev. E
56
,
2213
(
1997
).
26.
F.
Baronio
,
A.
Degasperis
,
M.
Conforti
, and
S.
Wabnitz
,
Phys. Rev. Lett.
109
,
044102
(
2012
).
27.
G. B.
Ling
and
L. L.
Ming
,
Chin. Phys. Lett.
28
,
110202
(
2011
).
28.
L. C.
Zhao
and
L.
Liu L
,
J. Opt. Soc. Am. B
29
,
3119
(
2012
).
29.
L. M.
Ling
,
B. L.
Guo
, and
L. C.
Zhao
,
Phys. Rev. E
89
,
041201(R)
(
2014
).
30.
L. C.
Zhao
,
B. L.
Guo
, and
L. M.
Ling
,
J. Math. Phys.
57
,
043508
(
2016
).
31.
L. M.
Ling
,
L. C.
Zhao
, and
B. L.
Guo
,
Commun. Nonlinear Sci. Numer. Simulat.
32
,
285
(
2016
).
32.
J. H.
Li
,
H. N.
Chan
,
K. S.
Chiang
, and
K. W.
Chow
,
Commun. Nonlinear Sci. Numer. Simulat.
28
,
28
(
2015
).
33.
S.
Chen
and
D.
Mihalache
,
J. Phys. A Math. Theor.
48
,
215202
(
2015
).
34.
G.
Zhang
,
Z.
Yan
,
X. Y.
Wen
, and
Y.
Chen
,
Phys. Rev. E
95
,
042201
(
2017
).
35.
R.
Radha
,
P. S.
Vinayagam
, and
K.
Porsezian
,
Commun. Nonlinear Sci. Numer. Simulat.
37
,
354
(
2016
).
36.
Y. H.
Qin
,
L. C.
Zhao
,
Z. Y.
Yang
, and
W. L.
Yang
,
Chaos
28
,
013111
(
2018
).
37.
Emergent Nonlinear Phenomena in Bose-Einstein Condensates: Theory and Experiment, edited by P. G. Kevrekidis, D. J. Frantzeskakis, and R. C. González (Springer, Berlin, 2008).
38.
V. G.
Makhankov
and
O. K.
Pashaev
,
Theor. Math. Phys.
53
,
979
(
1982
).
39.
X.
and
M.
Peng
,
Nonlinear Dyn.
73
,
405
(
2013
).
40.
D. S.
Wang
,
D. J.
Zhang
, and
J.
Yang
,
J. Math. Phys.
51
,
023510
(
2010
).
41.
N.
Vishnu Priya
and
M.
Senthilvelan
,
Commun. Nonlinear Sci. Numer. Simulat.
36
,
366
(
2016
).
42.
N.
Vishnu Priya
,
M.
Senthilvelan
, and
M.
Lakshmanan
,
Phys. Rev. E
89
,
062901
(
2014
).
43.
N.
Vishnu Priya
and
M.
Senthilvelan
,
Phys. Scr.
90
,
025203
(
2015
).
44.
N.
Vishnu Priya
and
M.
Senthilvelan
,
Commun. Nonlinear Sci. Numer. Simul.
20
,
401
(
2015
).
45.
N.
Vishnu Priya
and
M.
Senthilvelan
,
Wave Motion
54
,
125
(
2015
).
46.
S. P. T.
Mukam
,
V. K.
Kuetche
, and
T. B.
Bouetou
,
Eur. Phys. J. Plus
132
,
182
(
2017
).
47.
A.
Agalarov
,
V.
Zhulego
, and
T.
Gadzhimuradov
,
Phys. Rev. E
91
,
042909
(
2015
).
48.
Y. Q.
Yuan
,
B.
Tian
,
L.
Liu
, and
Y.
Sun
,
Europhys. Lett.
120
,
30001
(
2017
).
49.
Y. Q.
Yuan
,
B.
Tian
,
H. P.
Chai
,
X. Y.
Wu
, and
Z.
Du
,
Appl. Math. Lett.
87
,
50
(
2019
).
50.
Y. S.
Kivshar
and
G.
Agrawal
,
Optical Solitons: From Fibers to Photonic Crystals
(
Academic Press
,
London
,
2003
).
51.
D. M.
Pepper
,
J.
AuYeung
,
D.
Fekete
, and
A.
Yariv
,
Opt. Lett.
3
,
7
(
1978
).
52.
A.
Yariv
,
Quantum Electronics
(
John Wiley & Sons
,
New York
,
1989
).
53.
H. J.
Gerritsen
,
Appl. Phys. Lett.
10
,
239
(
1967
).
54.
T.
Yajima
and
H.
Souma
,
Phys. Rev. A
17
,
309
(
1978
).
55.
O. C.
Wright
,
Appl. Math. Lett.
16
,
647
(
2003
).
56.
A.
Jeffrey
and
D.
Zwillenger
,
Table of Integrals, Series and Products
(
Academic Press
,
New York
,
2007
).
57.
W.
Zhao
and
E.
Bourkoff
,
Opt. Lett.
14
,
703
(
1989
).
58.
M.
Onorato
,
D.
Proment
,
G.
Clauss
, and
M.
Klein
,
PLoS One
8
,
e54629
(
2013
).
You do not currently have access to this content.