TY - JOUR
T1 - New classes of solutions in the coupled PT symmetric nonlocal nonlinear Schrödinger equations with four wave mixing
AU - Vinayagam, P. S.
AU - Radha, R.
AU - Al Khawaja, U.
AU - Ling, Liming
N1 - Funding Information:
UAK and PSV acknowledge the support of UAE University through the grant UAEU-UPAR(7) and UAEU-UPAR(4). RR wishes to acknowledge the financial assistance received from Department of Atomic Energy-National Board for Higher Mathematics (DAE-NBHM) (No. NBHM/R.P.16/2014) and Council of Scientific and Industrial Research (CSIR) No. (03(1323)/14/EMR-II) for the financial support in the form Major Research Projects. LL acknowledge the financial support received from National Natural Science Foundation of China (Contact No. 11401221).
Funding Information:
UAK and PSV acknowledge the support of UAE University through the grant UAEU-UPAR(7) and UAEU-UPAR(4) . RR wishes to acknowledge the financial assistance received from Department of Atomic Energy-National Board for Higher Mathematics (DAE-NBHM) (No. NBHM/R.P.16/2014) and Council of Scientific and Industrial Research (CSIR) No. ( 03(1323)/14/EMR-II ) for the financial support in the form Major Research Projects. LL acknowledge the financial support received from National Natural Science Foundation of China (Contact No. 11401221 ).
Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2018/6
Y1 - 2018/6
N2 - We investigate generalized nonlocal coupled nonlinear Schorödinger equation containing Self-Phase Modulation, Cross-Phase Modulation and four wave mixing involving nonlocal interaction. By means of Darboux transformation we obtained a family of exact breathers and solitons including the Peregrine soliton, Kuznetsov-Ma breather, Akhmediev breather along with all kinds of soliton-soliton and breather-soltion interactions. We analyze and emphasize the impact of the four-wave mixing on the nature and interaction of the solutions. We found that the presence of four wave mixing converts a two-soliton solution into an Akhmediev breather. In particular, the inclusion of four wave mixing results in the generation of a new solutions which is spatially and temporally periodic called “Soliton (Breather) lattice”.
AB - We investigate generalized nonlocal coupled nonlinear Schorödinger equation containing Self-Phase Modulation, Cross-Phase Modulation and four wave mixing involving nonlocal interaction. By means of Darboux transformation we obtained a family of exact breathers and solitons including the Peregrine soliton, Kuznetsov-Ma breather, Akhmediev breather along with all kinds of soliton-soliton and breather-soltion interactions. We analyze and emphasize the impact of the four-wave mixing on the nature and interaction of the solutions. We found that the presence of four wave mixing converts a two-soliton solution into an Akhmediev breather. In particular, the inclusion of four wave mixing results in the generation of a new solutions which is spatially and temporally periodic called “Soliton (Breather) lattice”.
KW - Breathers
KW - Coupled nonlinear Schrödinger system
KW - Darboux transformation
KW - Four-wave mixing
KW - Lax pair
KW - Soliton
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U2 - 10.1016/j.cnsns.2017.11.016
DO - 10.1016/j.cnsns.2017.11.016
M3 - Article
AN - SCOPUS:85037540327
SN - 1007-5704
VL - 59
SP - 387
EP - 395
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
ER -