Step-like initial value problem and Whitham modulation in fluid dynamics to a generalized derivative nonlinear Schrödinger equation
In this paper, we study the step-like initial value problem for a generalized derivative nonlinear Schrödinger equation using the Whitham modulation theory. First, we utilize the finite-gap integration method to obtain the periodic solutions and the relevant Whitham equations for the 0-, 1-, and 2-g...
Saved in:
| Published in | Physics of fluids (1994) Vol. 36; no. 6 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Melville
American Institute of Physics
01.06.2024
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | In this paper, we study the step-like initial value problem for a generalized derivative nonlinear Schrödinger equation using the Whitham modulation theory. First, we utilize the finite-gap integration method to obtain the periodic solutions and the relevant Whitham equations for the 0-, 1-, and 2-genus cases used to characterize dispersive shock waves (DSWs). Second, we investigate four fundamental waves: two rarefaction waves (RWs) and two DSWs with step-like initial data. On this basis, we show the effect of varying certain parameters on the dynamics of the fluid model. We find that the boundary value, amplitude, and shape of the wave pattern in the fluid dynamics model will be significantly impacted by these parameters. Third, under two step-like initial data, waves are divided into six cases, which are actually combinations of DSWs and RWs. Finally, the dam break problem is explored to prove the effectiveness of the Whitham modulation theory in physical applications. |
|---|---|
| AbstractList | In this paper, we study the step-like initial value problem for a generalized derivative nonlinear Schrödinger equation using the Whitham modulation theory. First, we utilize the finite-gap integration method to obtain the periodic solutions and the relevant Whitham equations for the 0-, 1-, and 2-genus cases used to characterize dispersive shock waves (DSWs). Second, we investigate four fundamental waves: two rarefaction waves (RWs) and two DSWs with step-like initial data. On this basis, we show the effect of varying certain parameters on the dynamics of the fluid model. We find that the boundary value, amplitude, and shape of the wave pattern in the fluid dynamics model will be significantly impacted by these parameters. Third, under two step-like initial data, waves are divided into six cases, which are actually combinations of DSWs and RWs. Finally, the dam break problem is explored to prove the effectiveness of the Whitham modulation theory in physical applications. |
| Author | Liu, Bingyu Li Xinyue Zhao Qiulan |
| Author_xml | – sequence: 1 givenname: Bingyu surname: Liu fullname: Liu, Bingyu – sequence: 2 fullname: Zhao Qiulan – sequence: 3 fullname: Li Xinyue |
| BookMark | eNotkE1OwzAQhS1UJNrCghtYYoeUYseJkyxRxZ9UiUVBLKOJPW1dHKd1kkplzZm4ABfDpV3NSO_TmzdvRAaucUjINWcTzqS4Sycs5iyXyRkZhllEmZRycNgzFkkp-AUZte2aMSaKWA7J97zDTWTNJ1LjTGfA0h3YHunGN5XFmoLT9GNluhXUtG50b6EzjQswXdjeaKr3DmqjWto1FOgSHXqw5guDgt7sAr1DGkJa4xA8nauV__3Rxi3RU9z2_26X5HwBtsWr0xyT98eHt-lzNHt9epnez6INT_IuKrTmKWjMBM-1ZDpPVVEBKMY1qoXScVHwXMSgUpWJSnIVVxVLUhAqgXgRpDG5OfqG57Y9tl25bnrvwslSMJmyrJAiDdTtkWqV6f7zlRtvavD7krPy0HKZlqeWxR_GL3R6 |
| CODEN | PHFLE6 |
| ContentType | Journal Article |
| Copyright | Author(s) 2024 Author(s). Published under an exclusive license by AIP Publishing. |
| Copyright_xml | – notice: Author(s) – notice: 2024 Author(s). Published under an exclusive license by AIP Publishing. |
| DBID | 8FD H8D L7M |
| DOI | 10.1063/5.0210864 |
| DatabaseName | Technology Research Database Aerospace Database Advanced Technologies Database with Aerospace |
| DatabaseTitle | Technology Research Database Aerospace Database Advanced Technologies Database with Aerospace |
| DatabaseTitleList | Technology Research Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Physics |
| EISSN | 1089-7666 |
| GrantInformation_xml | – fundername: Shandong University of Science and Technology grantid: Jingying Project funderid: 10.13039/501100004295 |
| GroupedDBID | -~X 0ZJ 1UP 2-P 29O 2WC 4.4 5VS 6TJ AAAAW AABDS AAEUA AAPUP AAYIH ABJNI ACBRY ACGFS ACLYJ ACNCT ACZLF ADCTM AEJMO AENEX AFATG AFFNX AFHCQ AGKCL AGLKD AGMXG AGTJO AHSDT AIDUJ AJJCW AJQPL ALEPV ALMA_UNASSIGNED_HOLDINGS ATXIE AWQPM BPZLN CS3 DU5 EBS EJD ESX F5P FDOHQ FFFMQ HAM H~9 M6X M71 M73 NEUPN NPSNA O-B P2P RDFOP RIP RNS ROL RQS SC5 TN5 UCJ UQL WH7 XJT ~02 8FD BDMKI H8D L7M |
| ID | FETCH-LOGICAL-p148t-9dd15ade7318d60d85c9baac01decfcd2991832ac5c73b61c2bb045a3c4a2f183 |
| ISSN | 1070-6631 |
| IngestDate | Thu Oct 10 19:25:15 EDT 2024 Tue Jun 25 16:20:39 EDT 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 6 |
| Language | English |
| License | Published under an exclusive license by AIP Publishing. |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-p148t-9dd15ade7318d60d85c9baac01decfcd2991832ac5c73b61c2bb045a3c4a2f183 |
| ORCID | 0000-0003-0785-8328 0000-0002-5191-6604 |
| PQID | 3065079635 |
| PQPubID | 2050667 |
| PageCount | 13 |
| ParticipantIDs | proquest_journals_3065079635 scitation_primary_10_1063_5_0210864 |
| PublicationCentury | 2000 |
| PublicationDate | 20240600 20240601 |
| PublicationDateYYYYMMDD | 2024-06-01 |
| PublicationDate_xml | – month: 06 year: 2024 text: 20240600 |
| PublicationDecade | 2020 |
| PublicationPlace | Melville |
| PublicationPlace_xml | – name: Melville |
| PublicationTitle | Physics of fluids (1994) |
| PublicationYear | 2024 |
| Publisher | American Institute of Physics |
| Publisher_xml | – name: American Institute of Physics |
| References | Ma (c27) 2024 Geng, Dai (c28) 1999 Kaup, Newell (c21) 1978 Chen, Lee, Liu (c22) 1979 Ma (c20) 2024 Ma (c19) 2024 Ma (c29) 2024 Ivanov, Kamchatnov, Congy (c18) 2017 Biondini (c14) 2018 El, Hoefer (c1) 2016 Bai, Li, Zhao (c11) 2024 Hoefer, Smyth, Sprenger (c12) 2019 Gerdjikov, Ivanov (c23) 1983 Abeya, Biondini, Hoefer (c15) 2023 Gurevich, Pitaevskii (c6) 1974 Scotti, Pineda (c3) 2004 Luke (c10) 1966 Flaschka, Forest, McLaughlin (c9) 1980 Whitham (c5) 1965 Clarke, Smith, Reid (c2) 1981 Li, Han, Zhao (c26) 2022 Ma (c30) 2017 Lax, Levermore (c7) 1983 Zhang, Hao (c13) 2023 El, Geogjaev, Gurevich, Krylov (c16) 1995 Whitham (c8) 1965 Shukla, Eliasson (c4) 2010 Ivanov (c25) 2020 Geng, Jia, Xue, Zhai (c31) 2024 Gao, Wang (c24) 2023 |
| References_xml | – start-page: 11 year: 2016 ident: c1 article-title: Dispersive shock waves and modulation theory publication-title: Physica D contributor: fullname: Hoefer – start-page: 025701 year: 2023 ident: c15 article-title: Whitham modulation theory for the defocusing nonlinear Schrödinger equation in two and three spatial dimensions publication-title: J. Phys. A contributor: fullname: Hoefer – start-page: 106612 year: 2022 ident: c26 article-title: Interactions of localized wave and dynamics analysis in generalized derivative nonlinear Schrödinger equation publication-title: Commun. Nonlinear Sci. Numer. Simul. contributor: fullname: Zhao – start-page: 109025 year: 2024 ident: c29 article-title: A four-component hierarchy of combined integrable equations with bi-Hamiltonian formulations publication-title: Appl. Math. Lett. contributor: fullname: Ma – start-page: 114731 year: 2024 ident: c11 article-title: Evolution of dispersive shock waves to the complex modified Korteweg–de Vries equation with higher-order effects publication-title: Chaos, Solitons Fractals contributor: fullname: Zhao – start-page: 052220 year: 2018 ident: c14 article-title: Riemann problems and dispersive shocks in self-focusing media publication-title: Phys. Rev. E contributor: fullname: Biondini – start-page: 273 year: 1965 ident: c8 article-title: A general approach to linear and non-linear dispersive waves using a Lagrangian publication-title: J. Fluid Mech. contributor: fullname: Whitham – start-page: 105 year: 2024 ident: c20 article-title: Type (λ ,λ) reduced nonlocal integrable AKNS equations and their soliton solutions publication-title: Appl. Numer. Math. contributor: fullname: Ma – start-page: 114539 year: 2024 ident: c19 article-title: Binary Darboux transformation of vector nonlocal reverse-time integrable NLS equations publication-title: Chaos, Solitons Fractals contributor: fullname: Ma – start-page: 024222 year: 2023 ident: c24 article-title: Optical undular bores in Riemann problem of photon fluid with quintic nonlinearity publication-title: Phys. Rev. E contributor: fullname: Wang – start-page: 053827 year: 2020 ident: c25 article-title: Riemann problem for the light pulses in optical fibers for the generalized Chen-Lee-Liu equation publication-title: Phys. Rev. A contributor: fullname: Ivanov – start-page: 490 year: 1979 ident: c22 article-title: Integrability of nonlinear Hamiltonian systems by inverse scattering method publication-title: Phys. Scr. contributor: fullname: Liu – start-page: 062202 year: 2017 ident: c18 article-title: Solution of the Riemann problem for polarization waves in a two-component Bose-Einstein condensate publication-title: Phys. Rev. E contributor: fullname: Congy – start-page: 238 year: 1965 ident: c5 article-title: Nonlinear dispersive waves publication-title: Proc. R. Soc. A contributor: fullname: Whitham – start-page: 0233 year: 2017 ident: c30 article-title: Trigonal curves and algebro-geometric solutions to soliton hierarchies II publication-title: Proc. R. Soc. A contributor: fullname: Ma – start-page: L22307 year: 2004 ident: c3 article-title: Observation of very large and steep internal waves of elevation near the Massachusetts coast publication-title: Geophys. Res. Lett. contributor: fullname: Pineda – start-page: 219 year: 2019 ident: c12 article-title: Modulation theory solution for nonlinearly resonant, fifth-order Korteweg–de Vries, nonclassical, traveling dispersive shock waves publication-title: Stud. Appl. Math. contributor: fullname: Sprenger – start-page: 51 year: 2010 ident: c4 article-title: Nonlinear aspects of quantum plasma physics publication-title: Phys. Usp. contributor: fullname: Eliasson – start-page: 12461 year: 2023 ident: c13 article-title: Whitham modulation theory and periodic solutions for the fifth-order nonlinear Schrödinger equation in the Heisenberg ferromagnetic spin chain publication-title: Nonlinear Dyn. contributor: fullname: Hao – start-page: 130 year: 1983 ident: c23 article-title: The quadratic bundle of general form and the nonlinear evolution equations publication-title: Bulg. J. Phys. contributor: fullname: Ivanov – start-page: 291 year: 1974 ident: c6 article-title: Nonstationary structure of a collisionless shock wave publication-title: Sov. Phys. JETP contributor: fullname: Pitaevskii – start-page: 798 year: 1978 ident: c21 article-title: An exact solution for a derivative nonlinear Schrödinger equation publication-title: J. Math. Phys. contributor: fullname: Newell – start-page: 927 year: 2024 ident: c27 article-title: A generalized hierarchy of combined integrable bi-Hamiltonian equations from a specific fourth-order matrix spectral problem publication-title: Mathematics contributor: fullname: Ma – start-page: 26 year: 1999 ident: c28 article-title: Nonlinearization of the 33 matrix eigenvalue problem related to coupled nonlinear Schrödinger equations publication-title: J. Math. Anal. Appl. contributor: fullname: Dai – start-page: 739 year: 1980 ident: c9 article-title: Multiphase averaging and the inverse spectral solution of the Korteweg–de Vries equation publication-title: Commun. Pure Appl. Math. contributor: fullname: McLaughlin – start-page: 253 year: 1983 ident: c7 article-title: The small dispersion limit of the Korteweg-de Vries equation publication-title: Commun. Pure Appl. Math. contributor: fullname: Levermore – start-page: 1726 year: 1981 ident: c2 article-title: The morning glory of the Gulf of Carpentaria: An atmospheric undular bore publication-title: Mon. Weather Rev. contributor: fullname: Reid – start-page: 403 year: 1966 ident: c10 article-title: A perturbation method for nonlinear dispersive wave problems publication-title: Proc. R. Soc. A contributor: fullname: Luke – start-page: 186 year: 1995 ident: c16 article-title: Decay of an initial discontinuity in the defocusing NLS hydrodynamics publication-title: Physica D contributor: fullname: Krylov – start-page: 30 year: 2024 ident: c31 article-title: Application of tetragonal curves to coupled Boussinesq equations publication-title: Lett. Math. Phys. contributor: fullname: Zhai |
| SSID | ssj0003926 |
| Score | 2.4794502 |
| Snippet | In this paper, we study the step-like initial value problem for a generalized derivative nonlinear Schrödinger equation using the Whitham modulation theory.... |
| SourceID | proquest scitation |
| SourceType | Aggregation Database Publisher |
| SubjectTerms | Boundary value problems Fluid dynamics Modulation Parameters Rarefaction Schrodinger equation Shock waves |
| Title | Step-like initial value problem and Whitham modulation in fluid dynamics to a generalized derivative nonlinear Schrödinger equation |
| URI | http://dx.doi.org/10.1063/5.0210864 https://www.proquest.com/docview/3065079635 |
| Volume | 36 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnZ3NbtQwEMctKKrgwsdCRWlBI9Fb5WV3EzvxsSBQVQlOrbS3aGI7YkW_aLMceuaZeIG-WGdsJ2mlPZReopXXG6_8syZ_T8YzQuw4jQ09F1EiPS1krspaGp956SdYGO8mReP4cPL3H3r_KD-Yq_lQ_DKcLmnrsb1aea7kIVSpjbjyKdn_INvflBroM_GlKxGm670Yc4iWPF784sQfi5Z935y7m48-hSox4cUAV8D7iSdc8iZV6mIXR3O8XLhdF8vRhyQPyMWU2UG1uCIN6ujv_4k5wU9jMg284Iyd4cX6Z-1i-kL_ezmATQo3hJTaECASBompoIzJO59DcjHM8iEUKllFsguSpEls8qmtNLLQsWRKZ0pjLpO0ZPRKC02SiKZVjXmvWer8sXgyIxOhQ9DlEJxDqk3HaNE4cJcTSmef-p_e2RM8JcEQYxduyYPDl-J50vWwFyG9Eo_86Ui8SBofkgW9HIn1ND-vxd-eHiR6EOhBogdEDxI9GOhRZwgTCx09aM8A4RY9GOhBTw-Y3vW_SA46cm_E0bevh1_2ZaqJIc9p49pK49xUofMF2WKnJ65U1tSIdjJ13jbWkbpgI41W2SKr9dTO6ppUO2Y2x1lDX22INRrZvxXgjVeILp8a73OSsTVSS0mKknvTnTfFdje_VVr0l1XGkr4gq602xcd-zqvzmBqlCiENOqtUlSC9u1evLfFsWHfbYq29WPr3JPba-kNYFzeNHFq0 |
| link.rule.ids | 315,783,787,27936,27937 |
| linkProvider | American Institute of Physics |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Step-like+initial+value+problem+and+Whitham+modulation+in+fluid+dynamics+to+a+generalized+derivative+nonlinear+Schr%C3%B6dinger+equation&rft.jtitle=Physics+of+fluids+%281994%29&rft.date=2024-06-01&rft.issn=1070-6631&rft.eissn=1089-7666&rft.volume=36&rft.issue=6&rft_id=info:doi/10.1063%2F5.0210864 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1070-6631&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1070-6631&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1070-6631&client=summon |