Lump-Type Solutions, Mixed Solutions and Rogue Waves for a (3+1)-Dimensional Variable-Coefficients Burgers Equation
In this work, we consider the (3+1)-dimensional Burgers equation with variable coefficients, which is frequently used to define the motion of solitary waves. Abundant lump waves are constructed by taking the ansatz as a rational function. Furthermore, mixed solutions utilizing lump waves, rogue wave...
Saved in:
Published in | Symmetry (Basel) Vol. 16; no. 7; p. 779 |
---|---|
Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Basel
MDPI AG
01.07.2024
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Abstract | In this work, we consider the (3+1)-dimensional Burgers equation with variable coefficients, which is frequently used to define the motion of solitary waves. Abundant lump waves are constructed by taking the ansatz as a rational function. Furthermore, mixed solutions utilizing lump waves, rogue waves, and kink solitons are obtained by combining the rational function with an exponential function, resulting in fission and fusion phenomena. |
---|---|
AbstractList | In this work, we consider the (3+1)-dimensional Burgers equation with variable coefficients, which is frequently used to define the motion of solitary waves. Abundant lump waves are constructed by taking the ansatz as a rational function. Furthermore, mixed solutions utilizing lump waves, rogue waves, and kink solitons are obtained by combining the rational function with an exponential function, resulting in fission and fusion phenomena. |
Audience | Academic |
Author | Wu, Jianwen Cheng, Xueping Cai, Yuejin |
Author_xml | – sequence: 1 givenname: Jianwen surname: Wu fullname: Wu, Jianwen – sequence: 2 givenname: Yuejin surname: Cai fullname: Cai, Yuejin – sequence: 3 givenname: Xueping surname: Cheng fullname: Cheng, Xueping |
BookMark | eNpNkUFv1DAQhS1UJErpiT9giQuopNgZO46PZSml0iIkKHC0JrG98iqJt3ZSsf8eL4ug48OMnt98svWek5MpTo6Ql5xdAmj2Lu9H3jDFlNJPyGnNFFSt1uLk0fyMnOe8ZaUkk6JhpySvl3FX3e13jn6LwzKHOOW39HP45ex_geJk6de4WRz9iQ8uUx8TRfoaLvib6kMY3ZSLDQf6A1PAbnDVKjrvQx_cNGf6fkkblzK9vl_wwHtBnnocsjv_28_I94_Xd6tP1frLze3qal31teZz1QqFnncclawFl0Jq1fiuBmE1ou6bGiQrVxI61mrfuRbAWcXA8dqqptNwRm6PXBtxa3YpjJj2JmIwf4SYNgbTHPrBGS4YdALr1oIQtumwtRwAAQtPCg-F9erI2qV4v7g8m21cUvlzNsBayRqupCiuy6NrgwUaJh_nhH051o2hL3H5UPSrloFSQqoD9uK40KeYc3L-3zM5M4dUzaNU4TfuwpP3 |
Cites_doi | 10.1088/1674-1056/ac2d22 10.1063/1.524208 10.1088/1674-1056/acb91c 10.1111/sapm.12472 10.7566/JPSJ.93.024006 10.1016/j.jmmm.2020.166590 10.1016/j.chaos.2021.110875 10.1007/s11071-021-06201-z 10.1016/S0960-0779(02)00481-2 10.1016/j.cnsns.2020.105628 10.1175/1520-0485(1997)027<0871:ANMOIT>2.0.CO;2 10.1007/978-0-387-89488-1 10.1088/1674-1056/abff31 10.1103/PhysRevLett.116.173901 10.1088/1674-1056/23/11/110203 10.1088/1751-8121/ab7136 10.3390/sym14061135 10.3390/math10132311 10.1142/S0217979220502689 10.1063/1.872545 10.1088/1402-4896/abf307 10.1088/1674-1056/ab44a3 10.1007/s11071-022-07248-2 10.1007/s002200050044 10.1080/00207160.2019.1685088 10.3390/sym15030626 10.1002/mma.8465 10.1142/S0217984921501074 10.3390/sym16010082 10.20944/preprints202310.1833.v1 10.1007/s11071-022-08191-y 10.1088/1674-1056/ab6964 10.7498/aps.69.20191308 10.1017/CBO9780511543043 10.1016/j.aml.2020.106271 10.1016/j.wavemoti.2023.103141 10.1016/j.chaos.2018.01.023 10.1007/s11071-018-4317-8 10.1088/0305-4470/10/12/002 |
ContentType | Journal Article |
Copyright | COPYRIGHT 2024 MDPI AG 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
Copyright_xml | – notice: COPYRIGHT 2024 MDPI AG – notice: 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
DBID | AAYXX CITATION 7SC 7SR 7U5 8BQ 8FD 8FE 8FG ABJCF ABUWG AFKRA AZQEC BENPR BGLVJ CCPQU DWQXO H8D HCIFZ JG9 JQ2 L6V L7M L~C L~D M7S PIMPY PQEST PQQKQ PQUKI PRINS PTHSS DOA |
DOI | 10.3390/sym16070779 |
DatabaseName | CrossRef Computer and Information Systems Abstracts Engineered Materials Abstracts Solid State and Superconductivity Abstracts METADEX Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central ProQuest Central Essentials ProQuest Central Technology Collection ProQuest One Community College ProQuest Central Korea Aerospace Database SciTech Premium Collection Materials Research Database ProQuest Computer Science Collection ProQuest Engineering Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional ProQuest Engineering Database ProQuest - Publicly Available Content Database ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Academic ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection DOAJ Directory of Open Access Journals |
DatabaseTitle | CrossRef Publicly Available Content Database Materials Research Database Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central China ProQuest Central Aerospace Database Engineered Materials Abstracts ProQuest Engineering Collection ProQuest Central Korea Advanced Technologies Database with Aerospace Engineering Collection Engineering Database ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection METADEX Computer and Information Systems Abstracts Professional ProQuest One Academic UKI Edition Materials Science & Engineering Collection Solid State and Superconductivity Abstracts ProQuest One Academic |
DatabaseTitleList | Publicly Available Content Database CrossRef |
Database_xml | – sequence: 1 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website – sequence: 2 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
DeliveryMethod | fulltext_linktorsrc |
Discipline | Sciences (General) |
EISSN | 2073-8994 |
ExternalDocumentID | oai_doaj_org_article_1403b4a28d344d6ba8d133a3a70354f3 A803774573 10_3390_sym16070779 |
GroupedDBID | 5VS 8FE 8FG AADQD AAYXX ABDBF ABJCF ADBBV AFKRA AFZYC ALMA_UNASSIGNED_HOLDINGS BCNDV BENPR BGLVJ CCPQU CITATION E3Z ESX GROUPED_DOAJ GX1 HCIFZ IAO ITC J9A KQ8 L6V M7S MODMG M~E OK1 PIMPY PROAC PTHSS RIG TR2 TUS 7SC 7SR 7U5 8BQ 8FD ABUWG AZQEC DWQXO H8D JG9 JQ2 L7M L~C L~D PQEST PQQKQ PQUKI PRINS |
ID | FETCH-LOGICAL-c291t-847af1b1a75241545976fb234d9aa9c6235075253b089fbe833ed703e12d76b93 |
IEDL.DBID | BENPR |
ISSN | 2073-8994 |
IngestDate | Mon Jul 29 19:21:35 EDT 2024 Sun Jul 28 09:30:42 EDT 2024 Tue Aug 06 04:51:10 EDT 2024 Fri Aug 23 05:01:37 EDT 2024 |
IsDoiOpenAccess | true |
IsOpenAccess | true |
IsPeerReviewed | true |
IsScholarly | true |
Issue | 7 |
Language | English |
LinkModel | DirectLink |
MergedId | FETCHMERGED-LOGICAL-c291t-847af1b1a75241545976fb234d9aa9c6235075253b089fbe833ed703e12d76b93 |
OpenAccessLink | https://www.proquest.com/docview/3085061754/abstract/?pq-origsite=%requestingapplication% |
PQID | 3085061754 |
PQPubID | 2032326 |
ParticipantIDs | doaj_primary_oai_doaj_org_article_1403b4a28d344d6ba8d133a3a70354f3 proquest_journals_3085061754 gale_infotracacademiconefile_A803774573 crossref_primary_10_3390_sym16070779 |
PublicationCentury | 2000 |
PublicationDate | 2024-07-01 |
PublicationDateYYYYMMDD | 2024-07-01 |
PublicationDate_xml | – month: 07 year: 2024 text: 2024-07-01 day: 01 |
PublicationDecade | 2020 |
PublicationPlace | Basel |
PublicationPlace_xml | – name: Basel |
PublicationTitle | Symmetry (Basel) |
PublicationYear | 2024 |
Publisher | MDPI AG |
Publisher_xml | – name: MDPI AG |
References | Chen (ref_5) 2020; 69 Wu (ref_21) 2020; 34 Wang (ref_6) 2022; 31 Holloway (ref_26) 1997; 27 Bertini (ref_30) 1997; 183 Chen (ref_7) 2022; 148 Ma (ref_18) 2023; 32 Li (ref_23) 2022; 108 Zhang (ref_14) 2019; 28 ref_11 Shi (ref_9) 2023; 119 Joseph (ref_1) 1977; 10 Yang (ref_27) 2021; 30 Yan (ref_33) 2020; 104 ref_19 ref_17 ref_38 Wang (ref_10) 2020; 53 Hao (ref_16) 2023; 111 Zhang (ref_34) 2003; 17 Gao (ref_28) 2021; 147 Satsuma (ref_12) 1979; 20 Liu (ref_31) 2014; 23 Chen (ref_37) 2021; 95 Zhang (ref_41) 2018; 93 Baronio (ref_13) 2016; 116 Chen (ref_22) 2021; 96 ref_24 Das (ref_3) 1997; 4 ref_40 Zhang (ref_29) 2021; 103 ref_2 Hu (ref_8) 2022; 45 Liu (ref_36) 2020; 29 Jin (ref_20) 2020; 502 Wu (ref_15) 2022; 12 Wang (ref_39) 2019; 97 Hu (ref_32) 2018; 108 Gao (ref_35) 2021; 35 ref_4 Yan (ref_25) 2024; 92 |
References_xml | – volume: 31 start-page: 020501 year: 2022 ident: ref_6 article-title: Soliton fusion and fission for the high-order coupled nonlinear Schrödinger system in fiber lasers publication-title: Chin. Phys. B doi: 10.1088/1674-1056/ac2d22 contributor: fullname: Wang – volume: 20 start-page: 1496 year: 1979 ident: ref_12 article-title: Two-dimensional lumps in nonlinear dispersive systems publication-title: J. Math. Phys. doi: 10.1063/1.524208 contributor: fullname: Satsuma – volume: 32 start-page: 060201 year: 2023 ident: ref_18 article-title: Interaction solutions for the second extended (3+1)-dimensional Jimbo–Miwa equation publication-title: Chin. Phys. B doi: 10.1088/1674-1056/acb91c contributor: fullname: Ma – volume: 148 start-page: 1180 year: 2022 ident: ref_7 article-title: Riemann–Hilbert approach for discrete sine-Gordon equation with simple and double poles publication-title: Stud. Appl. Math. doi: 10.1111/sapm.12472 contributor: fullname: Chen – volume: 92 start-page: 024006 year: 2024 ident: ref_25 article-title: General multi-breather, high-order lump and semi-rational solutions of the (2+1)-dimensional Mel’nikov equation publication-title: J. Phys. Soc. Jpn. doi: 10.7566/JPSJ.93.024006 contributor: fullname: Yan – volume: 502 start-page: 166590 year: 2020 ident: ref_20 article-title: Rogue wave, interaction solutions to the KMM system publication-title: J. Magn. Magn. Mater. doi: 10.1016/j.jmmm.2020.166590 contributor: fullname: Jin – volume: 147 start-page: 110875 year: 2021 ident: ref_28 article-title: Beholding the shallow water waves near an ocean beach or in a lake via a Boussinesq-Burgers system publication-title: Chaos Soliton Fract. doi: 10.1016/j.chaos.2021.110875 contributor: fullname: Gao – volume: 103 start-page: 1891 year: 2021 ident: ref_29 article-title: An extended continuum mixed traffic model publication-title: Nonlinear Dyn. doi: 10.1007/s11071-021-06201-z contributor: fullname: Zhang – volume: 17 start-page: 669 year: 2003 ident: ref_34 article-title: Soliton-like and period form solutions for high dimensional nonlinear evolution equations publication-title: Chaos Soliton Fract. doi: 10.1016/S0960-0779(02)00481-2 contributor: fullname: Zhang – volume: 95 start-page: 105628 year: 2021 ident: ref_37 article-title: Novel evolutionary behaviors of the mixed solutions to a generalized Burgers equation with variable coefficients publication-title: Commun. Nonlinear Sci. Numer. Simulat. doi: 10.1016/j.cnsns.2020.105628 contributor: fullname: Chen – volume: 27 start-page: 871 year: 1997 ident: ref_26 article-title: A nonlinear model of internal tide transformation on the Australian North West Shelf publication-title: J. Phys. Oceanogr. doi: 10.1175/1520-0485(1997)027<0871:ANMOIT>2.0.CO;2 contributor: fullname: Holloway – ident: ref_38 doi: 10.1007/978-0-387-89488-1 – ident: ref_40 – volume: 30 start-page: 110202 year: 2021 ident: ref_27 article-title: Analysis of the rogue waves in the blood based on the high-order NLS equations with variable coefficients publication-title: Chin. Phys. B doi: 10.1088/1674-1056/abff31 contributor: fullname: Yang – volume: 116 start-page: 173901 year: 2016 ident: ref_13 article-title: Optical Kerr spatiotemporal dark-lump dynamics of hydrodynamic origin publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.116.173901 contributor: fullname: Baronio – volume: 23 start-page: 110203 year: 2014 ident: ref_31 article-title: Bäcklund transformations for the Burgers equation via localization of residual symmetries publication-title: Chin. Phys. B doi: 10.1088/1674-1056/23/11/110203 contributor: fullname: Liu – volume: 53 start-page: 294003 year: 2020 ident: ref_10 article-title: The modified Camassa–Holm equation: Bäcklund transformation and nonlinear superposition formula publication-title: J. Phys. A Math. Theor. doi: 10.1088/1751-8121/ab7136 contributor: fullname: Wang – ident: ref_4 doi: 10.3390/sym14061135 – ident: ref_2 doi: 10.3390/math10132311 – volume: 34 start-page: 2050268 year: 2020 ident: ref_21 article-title: Interactions solutions of various-type rogue with multi-stripe solitons and breather lump for the (2+1)-dimensional Maccari’s system publication-title: Int. J. Mod. Phys. B doi: 10.1142/S0217979220502689 contributor: fullname: Wu – volume: 4 start-page: 2095 year: 1997 ident: ref_3 article-title: Explosion of soliton in a multicomponent plasma publication-title: Phys. Plasmas doi: 10.1063/1.872545 contributor: fullname: Das – volume: 96 start-page: 095201 year: 2021 ident: ref_22 article-title: Derivation and simulation of the M-lump solutions to two (2+1)-dimensional nonlinear equations publication-title: Phys. Scr. doi: 10.1088/1402-4896/abf307 contributor: fullname: Chen – volume: 28 start-page: 110201 year: 2019 ident: ref_14 article-title: Trajectory equation of a lump before and after collision with line, lump, and breather waves for (2+1)-dimensional Kadomtsev–Petviashvili equation publication-title: Chin. Phys. B doi: 10.1088/1674-1056/ab44a3 contributor: fullname: Zhang – volume: 108 start-page: 1617 year: 2022 ident: ref_23 article-title: New mixed solutions generated by velocity resonance in the (2+1)-dimensional Sawada–Kotera equation publication-title: Nonlinear Dyn. doi: 10.1007/s11071-022-07248-2 contributor: fullname: Li – volume: 183 start-page: 571 year: 1997 ident: ref_30 article-title: Stochastic Burgers and KPZ equations from particle systems publication-title: Commun. Math. Phys. doi: 10.1007/s002200050044 contributor: fullname: Bertini – volume: 97 start-page: 2178 year: 2019 ident: ref_39 article-title: Dynamics of kink solitary waves and lump waves with interaction phenomena in a generalized (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation publication-title: Int. J. Comput. Math. doi: 10.1080/00207160.2019.1685088 contributor: fullname: Wang – ident: ref_17 doi: 10.3390/sym15030626 – volume: 45 start-page: 11545 year: 2022 ident: ref_8 article-title: Riemann–Hilbert problem associated with the vector Lakshmanan–Porsezian–Daniel model in the birefringent optical fibers publication-title: Math. Method Appl. Sci. doi: 10.1002/mma.8465 contributor: fullname: Hu – volume: 35 start-page: 2150107 year: 2021 ident: ref_35 article-title: Lump-type solutions, interaction solutions, and periodic lump solutions of the generalized (3+1)-dimensional Burgers equation publication-title: Mod. Phys. Lett. B doi: 10.1142/S0217984921501074 contributor: fullname: Gao – ident: ref_19 doi: 10.3390/sym16010082 – ident: ref_24 doi: 10.20944/preprints202310.1833.v1 – volume: 12 start-page: 230 year: 2022 ident: ref_15 article-title: Soliton, breather and lump molecules in the (2+1)-dimensional B-type Kadomtsev-Petviashvili-Korteweg De-Vries equation publication-title: Appl. Anal. Comput. contributor: fullname: Wu – volume: 111 start-page: 6701 year: 2023 ident: ref_16 article-title: Interaction phenomena between solitons, lumps and breathers for the combined KP3-4 equation publication-title: Nonlinear Dyn. doi: 10.1007/s11071-022-08191-y contributor: fullname: Hao – volume: 29 start-page: 030201 year: 2020 ident: ref_36 article-title: Lump and interaction solutions to the (3+1)-dimensional Burgers equation publication-title: Chin. Phys. B doi: 10.1088/1674-1056/ab6964 contributor: fullname: Liu – volume: 69 start-page: 014701 year: 2020 ident: ref_5 article-title: Rouge waves in fluid-filled elastic tube publication-title: Acta. Phys. Sin. doi: 10.7498/aps.69.20191308 contributor: fullname: Chen – ident: ref_11 doi: 10.1017/CBO9780511543043 – volume: 104 start-page: 106271 year: 2020 ident: ref_33 article-title: Soliton molecules in Sharma–Tasso–Olver–Burgers equation publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2020.106271 contributor: fullname: Yan – volume: 119 start-page: 103141 year: 2023 ident: ref_9 article-title: Exact solutions and Darboux transformation for the reverse space-time nonlocal Lakshmanan–Porsezian–Daniel equation publication-title: Wave Motion doi: 10.1016/j.wavemoti.2023.103141 contributor: fullname: Shi – volume: 108 start-page: 77 year: 2018 ident: ref_32 article-title: Residual symmetry, interaction solutions and consistent tanh expansion solvability for the third-order Burgers equation publication-title: Chaos Soliton Fract. doi: 10.1016/j.chaos.2018.01.023 contributor: fullname: Hu – volume: 93 start-page: 2169 year: 2018 ident: ref_41 article-title: General high-order rogue waves to nonlinear Schrödinger–Boussinesq equation with the dynamical analysis publication-title: Nonlinear Dyn. doi: 10.1007/s11071-018-4317-8 contributor: fullname: Zhang – volume: 10 start-page: L225 year: 1977 ident: ref_1 article-title: Solitary waves in a finite depth fluid publication-title: J. Phys. A Math. Gen. doi: 10.1088/0305-4470/10/12/002 contributor: fullname: Joseph |
SSID | ssj0000505460 |
Score | 2.346173 |
Snippet | In this work, we consider the (3+1)-dimensional Burgers equation with variable coefficients, which is frequently used to define the motion of solitary waves.... |
SourceID | doaj proquest gale crossref |
SourceType | Open Website Aggregation Database |
StartPage | 779 |
SubjectTerms | Burgers equation Exponential functions lump soliton solutions lump solutions Nonlinear equations Plasma physics Rational functions rogue waves Solitary waves variable-coefficients Burgers equation Water waves |
SummonAdditionalLinks | – databaseName: DOAJ Directory of Open Access Journals dbid: DOA link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrZ1LS8QwEMeDePIiPnF9kcOCu2iwbZI2PeqqLOJ6EF-3kFfBg7tqV9Fv70xTdS_ixWsIJcwknf-EmV8I6ZbeGiVdxQovcyYqWTDrfcIg8XHC-mClwUbh0WU-vBHn9_J-5qkvrAmLeOBouEPkyVlhMuW5ED6HL3tIqww3sFWlqCLnM5UzyVSkeoMUyZPYkMchrz-sPx6RpZYUWLQ1E4IaUv9v_-MmyJwtkcVWHdKjuKplMhfGK2S5PX817bWQ6P4qqS_ADwyzSPp9s3VARw_vwf8MUDP29AovZ-ideYMPgEKlhvb4ftpnJ8j1j0wOegsZM_ZQscEkNEwJLK-gx03LdE1PnyMPfI3cnJ1eD4asfUCBuaxMpwwij6lSm5pCYqAWkDzklc248KUxpQPlA2pQZpLbRJWVDYrz4MGuIc18kduSr5P58WQcNgjNpa-8kIkrHBeuUKXJPVeJFVnlVMpVh3S_bKqfIidDQ36Bptczpu-QY7T39xSEWzcD4HLdulz_5fIO2UNvaTyC0xfjTNtJACtFmJU-UgkHVSsLmLn95VDdns1a84bSB7JJbP7HarbIQgZCJ5bwbpP56ctr2AGhMrW7zZ78BHTI4-0 priority: 102 providerName: Directory of Open Access Journals |
Title | Lump-Type Solutions, Mixed Solutions and Rogue Waves for a (3+1)-Dimensional Variable-Coefficients Burgers Equation |
URI | https://www.proquest.com/docview/3085061754/abstract/ https://doaj.org/article/1403b4a28d344d6ba8d133a3a70354f3 |
Volume | 16 |
hasFullText | 1 |
inHoldings | 1 |
isFullTextHit | |
isPrint | |
link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1Lb9QwELb6uHBBLQ-xtKx8qEQrsDaJ7cQ5oW7Z7QrRClUU9mbZHgdxYLdtFgT_npnEu-0FLjk4VhSN5-2Zbxg7qsE7o0MjKtClUI2uhAfIBAY-QXmIXjtqFL64LGfX6sNcz7fYbN0LQ2WVa53YKWpYBsqRj2SHrYbGTo2cpyxAWI3e3dwKmh9F96xpmMY22y1yRRe2u-PJ5aerTb6FJrapMutb9CRG-qP2zw9CV8sqKuN6YJQ67P5_aejO7Ez32OPkL_LT_oD32VZcPGH7SSJbfpxgo0-esvYjnoyguJJvcl1v-cX33xHuF7hbAL-idA3_6n7hB9Bn5Y4fyzf5iXhPSP89Sgf_gjE0dVWJs2XsUCao4IKPuybqlk9ue4TwZ-x6Ovl8NhNppIIIRZ2vBNoi1-Q-d5Um060wnCgbX0gFtXN1QF8I_UNdaOkzUzc-GikjoFKIeQFV6Wv5nO0slov4gvFSQwNKZ6EKUoXK1K4EaTKviiaYXJoBO1rT1N70yBkWIw4ivX1A-gEbE703WwjuultY3n2zSXosgQp65QoDUikokb0AY2snHf6aVo0csNd0WpaEkljDpd4C_FOCt7KnJpPo5-oKdx6uD9QmaW3tPW-9_P_rA_aoQKemL9c9ZDuru5_xFTolKz9k22Z6PkxcN-xCe3yez_O_dtXkKw |
link.rule.ids | 315,786,790,870,2115,12792,21416,27957,27958,33408,33779,43635,43840,74392,74659 |
linkProvider | ProQuest |
linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1Lb9QwELagHOCCWh5iaWl9qEQrsJrEduKcqr6WBXZ7QC30Ztkep-LAbrtZEPx7ZhLvthe4OpZlzXiemfmGsd0avDM6NKICXQrV6Ep4gExg4BOUh-i1o0bhyXk5ulSfrvRVSri1qaxyqRM7RQ2zQDnyA9lhq6GxU4c3t4KmRtHf1TRC4yF7pCSaTuoUH35Y5VhoSpsqs74tT2J0f9D--UGIallFpVv3DFGH1_8vrdyZmuE6e5p8RH7UM3WDPYjTZ2wjSWHL9xJU9P5z1o6RG4JiSb7Kb73nk--_I9wtcDcF_oVSNPyb-4UHoJ_KHd-T7_J9cUro_j0yB_-KcTN1UomTWeyQJajIgh93jdMtP7vtUcFfsMvh2cXJSKQxCiIUdb4QaH9ck_vcVZrMtcIQomx8IRXUztUB_R_0CXWhpc9M3fhopIyAiiDmBVSlr-VLtjadTeMrxksNDSidhSpIFSpTuxKkybwqmmByaQZsd0lTe9OjZViMMoj09h7pB-yY6L3aQhDX3cJsfm2TxFgCEvTKFQakUlDikwKMp510eDWtGjlgb4lblgRxMXfBpX4CvClBWtkjk0n0bXWFO7eWDLVJQlt7955e___zDns8upiM7fjj-edN9qRAp6Yv191ia4v5z_gGnZKF3-5e3l-C3t8s |
linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1Lb9QwELaglRAX1PIQCwV8qEQrsDaJ7dg5oW67qwLtqqoo9Gb5iTiw2262CP49M4l32wtcEyuy5j2TmW8I2W2Cs1r6xFSQNRNJKuZCKBgkPl64EJ20OCh8Oq2PL8SnS3mZ-5_a3Fa5somdoQ5zjzXyIe-w1cDZiWHKbRFnR5MPV9cMN0jhn9a8TuM-2VSiliDhm6Px9Ox8XXHBnW2iLvohPQ65_rD98xPx1QqFjVx33FKH3v8vG905nskWeZQjRnrQs3ib3Iuzx2Q762RL9zJw9P4T0p4AbxhmlnRd7XpPT3_8juH2AbWzQM-xYEO_2V_wAYhaqaV7_F25z44Q67_H6aBfIYvGuSp2OI8dzgS2XNBRN0bd0vF1jxH-lFxMxl8Oj1leqsB81ZRLBt7IptKVVkl03gISijq5iovQWNt4iIYgQpSV5K7QTXJRcx4DmIVYVkHVruHPyMZsPovPCa1lSEHIwivPhVe6sXXgunCiSl6XXA_I7oqm5qrHzjCQcyDpzR3SD8gI6b0-goDX3YP54rvJ-mMQVtAJW-nAhQg1CFiA7NpyC1eTIvEBeYvcMqiWy4X1Nk8XwE0R4Moc6IJDpCsVnNxZMdRkfW3NrXS9-P_rN-QBiJ05-Tj9_JI8rCDC6Xt3d8jGcnETX0GEsnSvs-j9Bd8t5M8 |
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=Lump-Type+Solutions%2C+Mixed+Solutions+and+Rogue+Waves+for+a+%283%2B1%29-Dimensional+Variable-Coefficients+Burgers+Equation&rft.jtitle=Symmetry+%28Basel%29&rft.au=Wu%2C+Jianwen&rft.au=Cai%2C+Yuejin&rft.au=Cheng%2C+Xueping&rft.date=2024-07-01&rft.pub=MDPI+AG&rft.eissn=2073-8994&rft.volume=16&rft.issue=7&rft.spage=779&rft_id=info:doi/10.3390%2Fsym16070779&rft.externalDBID=HAS_PDF_LINK |
thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2073-8994&client=summon |
thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2073-8994&client=summon |
thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2073-8994&client=summon |