M- $truncated optical soliton and their characteristics to a nonlinear equation governing the certain instabilities of modulated wave trains

This study investigates the nonlinear Hamiltonian amplitude equation by using two analytical techniques, namely; the extended sinh-Gordon equation expansion method, and the extended rational sine-cosine/sinh-cosh methods. Some important wave solutions are successfully constructed, such as dark, brig...

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Published inAIMS mathematics Vol. 6; no. 9; pp. 9207 - 9221
Main Authors Yusuf, Abdullahi, Sulaiman, Tukur A., Inc, Mustafa, Abdel-Khalek, Sayed, Mahmoud, K. H.
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
extended rational sine-cosine/sinh-cosh
extended sinh-gordon method
hamiltonian amplitude equation
m-truncated derivative
optical solitons
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ISSN2473-6988
2473-6988
DOI10.3934/math.2021535

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Abstract This study investigates the nonlinear Hamiltonian amplitude equation by using two analytical techniques, namely; the extended sinh-Gordon equation expansion method, and the extended rational sine-cosine/sinh-cosh methods. Some important wave solutions are successfully constructed, such as dark, bright, combined dark-bright, singular solitons, periodic and singular periodic wave solutions. The physical features of the acquired solutions are plotted to depict the clear dynamical behaviour of the reported results. All the acquired solutions have satisfied the original equation.
AbstractList This study investigates the nonlinear Hamiltonian amplitude equation by using two analytical techniques, namely; the extended sinh-Gordon equation expansion method, and the extended rational sine-cosine/sinh-cosh methods. Some important wave solutions are successfully constructed, such as dark, bright, combined dark-bright, singular solitons, periodic and singular periodic wave solutions. The physical features of the acquired solutions are plotted to depict the clear dynamical behaviour of the reported results. All the acquired solutions have satisfied the original equation.
Author Sulaiman, Tukur A.
Mahmoud, K. H.
Inc, Mustafa
Abdel-Khalek, Sayed
Yusuf, Abdullahi
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crossref_primary_10_1371_journal_pone_0276961
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Cites_doi 10.1016/j.aml.2016.11.018
10.1007/BF00624671
10.1140/epjp/i2017-11655-9
10.1007/s12043-020-02070-0
10.1142/S0217979221500430
10.1017/CBO9780511623998
10.1364/OL.12.000355
10.1016/j.amc.2007.10.012
10.1088/1751-8113/44/30/305203
10.1016/j.ijleo.2018.02.043
10.1007/s11082-019-2116-1
10.1016/j.rinp.2021.103850
10.1103/PhysRevA.78.023821
10.1088/0253-6102/50/6/26
10.1016/j.rinp.2021.104228
10.1142/S0217979220501155
10.1103/PhysRevE.81.016605
10.1088/1402-4896/ab1791
10.1016/j.ijleo.2017.01.078
10.1007/s12043-012-0284-7
10.1098/rsta.1985.0043
10.3389/fphy.2020.00332
10.1016/j.rinp.2021.104177
10.1142/S0217984916503814
10.1142/S021988782050173X
10.1016/j.cnsns.2017.01.001
10.1119/1.17120
10.1016/j.amc.2006.11.143
10.1007/s11071-020-05561-2
10.1088/0951-7715/25/7/R73
10.1063/1.523737
10.1140/epjp/i2019-12545-x
10.1016/j.amc.2009.05.049
10.1016/j.aml.2016.11.012
10.1016/j.cnsns.2017.01.018
10.1088/0253-6102/50/5/06
10.1201/9781420035223
10.1016/B978-012410590-4/50012-7
10.3934/math.2020447
10.1143/JPSJ.61.1187
10.1007/s11071-018-4049-9
10.1103/PhysRevLett.27.1192
10.1016/j.aej.2014.06.005
10.1143/JPSJ.52.394
10.1016/j.spmi.2017.11.022
10.1016/B978-0-12-397023-7.00011-5
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CorporateAuthor Department of Computer Engineering, Biruni University, Istanbul, Turkey
Department of Mathematics, College of Science, P.O. Box 11099, Taif University, Taif 21944, Saudi Arabia
Department of Mathematics, Science Faculty, Firat University Elazig, Turkey
Department of Physics, College of Khurma University College, Taif University, P.O. Box11099, Taif 21944, Saudi Arabia
Department of Medical Research, China Medical University Hospital, China Medical University, 40402 Taichung, Taiwan
Department of Mathematics, Federal University Dutse, Jigawa, Nigeria
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References key-10.3934/math.2021535-16
key-10.3934/math.2021535-15
key-10.3934/math.2021535-14
key-10.3934/math.2021535-13
key-10.3934/math.2021535-12
key-10.3934/math.2021535-11
key-10.3934/math.2021535-10
key-10.3934/math.2021535-19
key-10.3934/math.2021535-18
key-10.3934/math.2021535-17
key-10.3934/math.2021535-7
key-10.3934/math.2021535-6
key-10.3934/math.2021535-51
key-10.3934/math.2021535-9
key-10.3934/math.2021535-50
key-10.3934/math.2021535-8
key-10.3934/math.2021535-3
key-10.3934/math.2021535-2
key-10.3934/math.2021535-5
key-10.3934/math.2021535-4
key-10.3934/math.2021535-49
key-10.3934/math.2021535-48
key-10.3934/math.2021535-1
key-10.3934/math.2021535-47
key-10.3934/math.2021535-46
key-10.3934/math.2021535-45
key-10.3934/math.2021535-44
key-10.3934/math.2021535-43
key-10.3934/math.2021535-42
key-10.3934/math.2021535-41
key-10.3934/math.2021535-40
key-10.3934/math.2021535-38
key-10.3934/math.2021535-37
key-10.3934/math.2021535-36
key-10.3934/math.2021535-35
key-10.3934/math.2021535-34
key-10.3934/math.2021535-33
key-10.3934/math.2021535-32
key-10.3934/math.2021535-31
key-10.3934/math.2021535-39
key-10.3934/math.2021535-30
key-10.3934/math.2021535-27
key-10.3934/math.2021535-26
key-10.3934/math.2021535-25
key-10.3934/math.2021535-24
key-10.3934/math.2021535-23
key-10.3934/math.2021535-22
key-10.3934/math.2021535-21
key-10.3934/math.2021535-20
key-10.3934/math.2021535-29
key-10.3934/math.2021535-28
References_xml – ident: key-10.3934/math.2021535-35
  doi: 10.1016/j.aml.2016.11.018
– ident: key-10.3934/math.2021535-5
  doi: 10.1007/BF00624671
– ident: key-10.3934/math.2021535-14
  doi: 10.1140/epjp/i2017-11655-9
– ident: key-10.3934/math.2021535-11
  doi: 10.1007/s12043-020-02070-0
– ident: key-10.3934/math.2021535-9
  doi: 10.1142/S0217979221500430
– ident: key-10.3934/math.2021535-22
  doi: 10.1017/CBO9780511623998
– ident: key-10.3934/math.2021535-3
  doi: 10.1364/OL.12.000355
– ident: key-10.3934/math.2021535-18
  doi: 10.1016/j.amc.2007.10.012
– ident: key-10.3934/math.2021535-17
  doi: 10.1088/1751-8113/44/30/305203
– ident: key-10.3934/math.2021535-37
  doi: 10.1016/j.ijleo.2018.02.043
– ident: key-10.3934/math.2021535-38
  doi: 10.1007/s11082-019-2116-1
– ident: key-10.3934/math.2021535-8
  doi: 10.1016/j.rinp.2021.103850
– ident: key-10.3934/math.2021535-30
  doi: 10.1103/PhysRevA.78.023821
– ident: key-10.3934/math.2021535-42
  doi: 10.1088/0253-6102/50/6/26
– ident: key-10.3934/math.2021535-40
  doi: 10.1016/j.rinp.2021.104228
– ident: key-10.3934/math.2021535-10
  doi: 10.1142/S0217979220501155
– ident: key-10.3934/math.2021535-31
  doi: 10.1103/PhysRevE.81.016605
– ident: key-10.3934/math.2021535-29
  doi: 10.1088/1402-4896/ab1791
– ident: key-10.3934/math.2021535-33
  doi: 10.1016/j.ijleo.2017.01.078
– ident: key-10.3934/math.2021535-44
  doi: 10.1007/s12043-012-0284-7
– ident: key-10.3934/math.2021535-49
– ident: key-10.3934/math.2021535-6
  doi: 10.1098/rsta.1985.0043
– ident: key-10.3934/math.2021535-24
  doi: 10.3389/fphy.2020.00332
– ident: key-10.3934/math.2021535-41
  doi: 10.1016/j.rinp.2021.104177
– ident: key-10.3934/math.2021535-39
  doi: 10.1142/S0217984916503814
– ident: key-10.3934/math.2021535-7
  doi: 10.1142/S021988782050173X
– ident: key-10.3934/math.2021535-28
  doi: 10.1016/j.cnsns.2017.01.001
– ident: key-10.3934/math.2021535-21
  doi: 10.1119/1.17120
– ident: key-10.3934/math.2021535-26
  doi: 10.1016/j.amc.2006.11.143
– ident: key-10.3934/math.2021535-32
  doi: 10.1007/s11071-020-05561-2
– ident: key-10.3934/math.2021535-4
  doi: 10.1088/0951-7715/25/7/R73
– ident: key-10.3934/math.2021535-15
  doi: 10.1063/1.523737
– ident: key-10.3934/math.2021535-48
  doi: 10.1140/epjp/i2019-12545-x
– ident: key-10.3934/math.2021535-13
  doi: 10.1016/j.amc.2009.05.049
– ident: key-10.3934/math.2021535-27
  doi: 10.1016/j.aml.2016.11.012
– ident: key-10.3934/math.2021535-34
  doi: 10.1016/j.cnsns.2017.01.018
– ident: key-10.3934/math.2021535-47
  doi: 10.1088/0253-6102/50/5/06
– ident: key-10.3934/math.2021535-51
  doi: 10.1201/9781420035223
– ident: key-10.3934/math.2021535-1
– ident: key-10.3934/math.2021535-2
  doi: 10.1016/B978-012410590-4/50012-7
– ident: key-10.3934/math.2021535-25
  doi: 10.3934/math.2020447
– ident: key-10.3934/math.2021535-50
– ident: key-10.3934/math.2021535-46
  doi: 10.1143/JPSJ.61.1187
– ident: key-10.3934/math.2021535-36
  doi: 10.1007/s11082-019-2116-1
– ident: key-10.3934/math.2021535-19
– ident: key-10.3934/math.2021535-45
  doi: 10.1007/s11071-018-4049-9
– ident: key-10.3934/math.2021535-23
  doi: 10.1103/PhysRevLett.27.1192
– ident: key-10.3934/math.2021535-43
  doi: 10.1016/j.aej.2014.06.005
– ident: key-10.3934/math.2021535-16
  doi: 10.1143/JPSJ.52.394
– ident: key-10.3934/math.2021535-12
  doi: 10.1016/j.spmi.2017.11.022
– ident: key-10.3934/math.2021535-20
  doi: 10.1016/B978-0-12-397023-7.00011-5
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SubjectTerms extended rational sine-cosine/sinh-cosh
extended sinh-gordon method
hamiltonian amplitude equation
m-truncated derivative
optical solitons
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Title M- $truncated optical soliton and their characteristics to a nonlinear equation governing the certain instabilities of modulated wave trains
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