Integrable Variable-coefficient Coupled Cylindrical NLS Equations and Their Explicit Solutions
Based on the generalized dressing method, we propose integrable variable coefficient coupled cylin-drical nonlinear SchrSdinger equations and their Lax pairs. As applications, their explicit solutions and their reductions are constructed.
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| Published in | Acta Mathematicae Applicatae Sinica Vol. 30; no. 4; pp. 1017 - 1024 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.10.2014
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0168-9673 1618-3932 |
| DOI | 10.1007/s10255-014-0439-z |
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| Abstract | Based on the generalized dressing method, we propose integrable variable coefficient coupled cylin-drical nonlinear SchrSdinger equations and their Lax pairs. As applications, their explicit solutions and their reductions are constructed. |
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| AbstractList | Based on the generalized dressing method, we propose integrable variable coefficient coupled cylin-drical nonlinear SchrSdinger equations and their Lax pairs. As applications, their explicit solutions and their reductions are constructed. Based on the generalized dressing method, we propose integrable variable coefficient coupled cylindrical nonlinear Schrödinger equations and their Lax pairs. As applications, their explicit solutions and their reductions are constructed. |
| Author | Ting SU Guo-hua DING Jian-yin FANG |
| AuthorAffiliation | Department of Mathematical and Physical Science, Henan Institute of Engineering, Zhengzhou 451191, China |
| Author_xml | – sequence: 1 givenname: Ting surname: Su fullname: Su, Ting email: suting1976@163.com organization: Department of Mathematical and Physical Science, Henan Institute of Engineering – sequence: 2 givenname: Guo-hua surname: Ding fullname: Ding, Guo-hua organization: Department of Mathematical and Physical Science, Henan Institute of Engineering – sequence: 3 givenname: Jian-yin surname: Fang fullname: Fang, Jian-yin organization: Department of Mathematical and Physical Science, Henan Institute of Engineering |
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| Cites_doi | 10.1063/1.533278 10.1016/0375-9601(89)90579-3 10.1007/BF01075696 10.1143/JPSJ.60.409 10.1103/PhysRevE.50.1543 10.1016/0375-9601(96)00208-3 10.1088/0266-5611/17/4/321 10.1103/PhysRevLett.78.646 10.1063/1.529732 10.1002/sapm1969484377 10.1364/OL.9.000288 10.1007/BF01077483 10.1088/0305-4470/17/16/001 10.1002/sapm1967461133 |
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| Copyright | Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2014 |
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| Keywords | variable-coefficient coupled NLS equations 45Gxx the generalized dressing method integrability 35Dxx |
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| Notes | 11-2041/O1 variable-coefficient coupled NLS equations; the generalized dressing method; integrability Based on the generalized dressing method, we propose integrable variable coefficient coupled cylin-drical nonlinear SchrSdinger equations and their Lax pairs. As applications, their explicit solutions and their reductions are constructed. |
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| References | DaiHHJeffreyAThe inverse scattering transforms for certain types of variable-coefficient KdV equationsPhys. Lett. A.198913936937210.1016/0375-9601(89)90579-31013316 HasegawaAGeneration of a train of soliton pulses by induced modulational instability in optical fibersOptics Letters1984928829010.1364/OL.9.000288 ChristodoulidesDNCoskunTHMitchellMSegevMTheory of Incoherent Self-focusing in Biased Photorefractive MediaPhys. Rev. Lett.19977864664910.1103/PhysRevLett.78.646 ZakharovVEShabatABIntegration of the nonlinear equations of mathematical physics by the method of the inverse scattering problem IIFunt. Anal. Appl.197913166174545363 SaSaNSatsumaJNew-type of soliton solutions for a higher-order nonlinear Schrödinger equationJ. Phys. Soc. Jpn.19916040941710.1143/JPSJ.60.4090920.351281104387 TasgalRSPotasekMJSoliton solutions to coupled higher-order nonlinear Schrödinger equationsJ. Math. Phys.1992331028121510.1063/1.5297321149244 ChowdhuryARBasakBOn the complete solution of the Hirota-Satsuma system through the ‘dressing’ operator techniqueJ. Phys. A.198417L863L86810.1088/0305-4470/17/16/0010559.35082 AgrawalGPBoydRWNonlinear Fiber Optics2001New YorkSpringer-Verlag BuryakAVKivsharYSParkerDFCoupling between dark and bright solitonsPhys. Lett. A.1996215576210.1016/0375-9601(96)00208-3 ZakharovVEShabatABExact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear mediaSov. Phys. JETP.1972346269406174 ParkerAA reformulation of the ‘dressing method’ for the Sawada-Kotera equationInverse Problems20011788589510.1088/0266-5611/17/4/3210983.351201861489 BenneyDJRoskesGJWave instabilitiesStud. Appl. Math.1969483773850216.52904 DyeJMParkerAAn inverse scattering scheme for the regularized long-wave equationJ. Math. Phys2000412889290410.1063/1.5332780973.351651755476 BenneyDJNewellACThe propagation of nonlinear wave envelopesJ. Math. Phys.1967461331390153.30301241052 ZakharovVEShabatABA scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem IFunt. Anal. Appl.1974822623510.1007/BF010756960303.35024 PorsezianKShanmughaSPMahalingamACoupled high-order nonlinear Schrödinger equations in nonlinear optics:Painlevé analysis and integrabilityPhys. Rev. E1994501543154710.1103/PhysRevE.50.15431381874 AgrawalGPNonlinear and Fiber Optics1989LondonAcadmic Press JeffreyADaiHHOn the application of a generalizzed version of the dressing method to the integration of variable-coefficient KdV equationRendiconti.di Mathematica, Serie VII1990104394550748.350401080309 GP Agrawal (439_CR2) 1989 VE Zakharov (439_CR17) 1979; 13 VE Zakharov (439_CR16) 1974; 8 DJ Benney (439_CR4) 1969; 48 A Hasegawa (439_CR10) 1984; 9 VE Zakharov (439_CR18) 1972; 34 AV Buryak (439_CR5) 1996; 215 DN Christodoulides (439_CR7) 1997; 78 AR Chowdhury (439_CR6) 1984; 17 A Jeffrey (439_CR11) 1990; 10 GP Agrawal (439_CR1) 2001 HH Dai (439_CR8) 1989; 139 N SaSa (439_CR14) 1991; 60 RS Tasgal (439_CR15) 1992; 33 DJ Benney (439_CR3) 1967; 46 JM Dye (439_CR9) 2000; 41 K Porsezian (439_CR13) 1994; 50 A Parker (439_CR12) 2001; 17 |
| References_xml | – reference: BuryakAVKivsharYSParkerDFCoupling between dark and bright solitonsPhys. Lett. A.1996215576210.1016/0375-9601(96)00208-3 – reference: ZakharovVEShabatABIntegration of the nonlinear equations of mathematical physics by the method of the inverse scattering problem IIFunt. Anal. Appl.197913166174545363 – reference: BenneyDJNewellACThe propagation of nonlinear wave envelopesJ. Math. Phys.1967461331390153.30301241052 – reference: DaiHHJeffreyAThe inverse scattering transforms for certain types of variable-coefficient KdV equationsPhys. Lett. A.198913936937210.1016/0375-9601(89)90579-31013316 – reference: AgrawalGPBoydRWNonlinear Fiber Optics2001New YorkSpringer-Verlag – reference: SaSaNSatsumaJNew-type of soliton solutions for a higher-order nonlinear Schrödinger equationJ. Phys. Soc. Jpn.19916040941710.1143/JPSJ.60.4090920.351281104387 – reference: DyeJMParkerAAn inverse scattering scheme for the regularized long-wave equationJ. Math. Phys2000412889290410.1063/1.5332780973.351651755476 – reference: ZakharovVEShabatABExact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear mediaSov. Phys. JETP.1972346269406174 – reference: AgrawalGPNonlinear and Fiber Optics1989LondonAcadmic Press – reference: ChristodoulidesDNCoskunTHMitchellMSegevMTheory of Incoherent Self-focusing in Biased Photorefractive MediaPhys. Rev. Lett.19977864664910.1103/PhysRevLett.78.646 – reference: ParkerAA reformulation of the ‘dressing method’ for the Sawada-Kotera equationInverse Problems20011788589510.1088/0266-5611/17/4/3210983.351201861489 – reference: PorsezianKShanmughaSPMahalingamACoupled high-order nonlinear Schrödinger equations in nonlinear optics:Painlevé analysis and integrabilityPhys. Rev. E1994501543154710.1103/PhysRevE.50.15431381874 – reference: ZakharovVEShabatABA scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem IFunt. Anal. Appl.1974822623510.1007/BF010756960303.35024 – reference: ChowdhuryARBasakBOn the complete solution of the Hirota-Satsuma system through the ‘dressing’ operator techniqueJ. Phys. A.198417L863L86810.1088/0305-4470/17/16/0010559.35082 – reference: HasegawaAGeneration of a train of soliton pulses by induced modulational instability in optical fibersOptics Letters1984928829010.1364/OL.9.000288 – reference: JeffreyADaiHHOn the application of a generalizzed version of the dressing method to the integration of variable-coefficient KdV equationRendiconti.di Mathematica, Serie VII1990104394550748.350401080309 – reference: BenneyDJRoskesGJWave instabilitiesStud. Appl. Math.1969483773850216.52904 – reference: TasgalRSPotasekMJSoliton solutions to coupled higher-order nonlinear Schrödinger equationsJ. Math. Phys.1992331028121510.1063/1.5297321149244 – volume: 41 start-page: 2889 year: 2000 ident: 439_CR9 publication-title: J. Math. Phys doi: 10.1063/1.533278 – volume-title: Nonlinear Fiber Optics year: 2001 ident: 439_CR1 – volume: 34 start-page: 62 year: 1972 ident: 439_CR18 publication-title: Sov. Phys. JETP. – volume: 139 start-page: 369 year: 1989 ident: 439_CR8 publication-title: Phys. Lett. A. doi: 10.1016/0375-9601(89)90579-3 – volume: 10 start-page: 439 year: 1990 ident: 439_CR11 publication-title: Rendiconti.di Mathematica, Serie VII – volume: 8 start-page: 226 year: 1974 ident: 439_CR16 publication-title: Funt. Anal. Appl. doi: 10.1007/BF01075696 – volume-title: Nonlinear and Fiber Optics year: 1989 ident: 439_CR2 – volume: 60 start-page: 409 year: 1991 ident: 439_CR14 publication-title: J. Phys. Soc. Jpn. doi: 10.1143/JPSJ.60.409 – volume: 50 start-page: 1543 year: 1994 ident: 439_CR13 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.50.1543 – volume: 215 start-page: 57 year: 1996 ident: 439_CR5 publication-title: Phys. Lett. A. doi: 10.1016/0375-9601(96)00208-3 – volume: 17 start-page: 885 year: 2001 ident: 439_CR12 publication-title: Inverse Problems doi: 10.1088/0266-5611/17/4/321 – volume: 78 start-page: 646 year: 1997 ident: 439_CR7 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.78.646 – volume: 33 start-page: 1028 year: 1992 ident: 439_CR15 publication-title: J. Math. Phys. doi: 10.1063/1.529732 – volume: 48 start-page: 377 year: 1969 ident: 439_CR4 publication-title: Stud. Appl. Math. doi: 10.1002/sapm1969484377 – volume: 9 start-page: 288 year: 1984 ident: 439_CR10 publication-title: Optics Letters doi: 10.1364/OL.9.000288 – volume: 13 start-page: 166 year: 1979 ident: 439_CR17 publication-title: Funt. Anal. Appl. doi: 10.1007/BF01077483 – volume: 17 start-page: L863 year: 1984 ident: 439_CR6 publication-title: J. Phys. A. doi: 10.1088/0305-4470/17/16/001 – volume: 46 start-page: 133 year: 1967 ident: 439_CR3 publication-title: J. Math. Phys. doi: 10.1002/sapm1967461133 |
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| Snippet | Based on the generalized dressing method, we propose integrable variable coefficient coupled cylin-drical nonlinear SchrSdinger equations and their Lax pairs.... Based on the generalized dressing method, we propose integrable variable coefficient coupled cylindrical nonlinear Schrödinger equations and their Lax pairs.... |
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| SubjectTerms | Applications of Mathematics Lax对 Math Applications in Computer Science Mathematical and Computational Physics Mathematics Mathematics and Statistics NLS方程 Theoretical 变系数 可积 圆柱 精确解 耦合 非线性 |
| Title | Integrable Variable-coefficient Coupled Cylindrical NLS Equations and Their Explicit Solutions |
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