Lax Formulation of 3-Component KP Hierarchy by Shiota Construction
It is quite basic in integrable systems to derive Lax equations from bilinear equations. For multi-component KP theory, corresponding Lax structures are mainly constructed by matrix pseudo-differential operators for fixed discrete variables, or by matrix difference operators for even-component cases...
Saved in:
| Published in | Journal of nonlinear science Vol. 35; no. 5 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.10.2025
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | It is quite basic in integrable systems to derive Lax equations from bilinear equations. For multi-component KP theory, corresponding Lax structures are mainly constructed by matrix pseudo-differential operators for fixed discrete variables, or by matrix difference operators for even-component cases. Here we use Shiota method to construct Lax structure of 3-component KP hierarchy and its reduction by introducing two shift operators
Λ
1
and
Λ
2
, where relations among different discrete variables can be easily found. We believe the results here are quite typical for general multi-component KP theory, which may be helpful for general cases. |
|---|---|
| AbstractList | It is quite basic in integrable systems to derive Lax equations from bilinear equations. For multi-component KP theory, corresponding Lax structures are mainly constructed by matrix pseudo-differential operators for fixed discrete variables, or by matrix difference operators for even-component cases. Here we use Shiota method to construct Lax structure of 3-component KP hierarchy and its reduction by introducing two shift operators
Λ
1
and
Λ
2
, where relations among different discrete variables can be easily found. We believe the results here are quite typical for general multi-component KP theory, which may be helpful for general cases. It is quite basic in integrable systems to derive Lax equations from bilinear equations. For multi-component KP theory, corresponding Lax structures are mainly constructed by matrix pseudo-differential operators for fixed discrete variables, or by matrix difference operators for even-component cases. Here we use Shiota method to construct Lax structure of 3-component KP hierarchy and its reduction by introducing two shift operators Λ1 and Λ2, where relations among different discrete variables can be easily found. We believe the results here are quite typical for general multi-component KP theory, which may be helpful for general cases. |
| ArticleNumber | 93 |
| Author | Cui, Tongtong Wang, Jinbiao Cao, Wenqi Cheng, Jipeng |
| Author_xml | – sequence: 1 givenname: Tongtong surname: Cui fullname: Cui, Tongtong organization: School of Mathematics, China University of Mining and Technology – sequence: 2 givenname: Jinbiao surname: Wang fullname: Wang, Jinbiao organization: School of Mathematics, China University of Mining and Technology – sequence: 3 givenname: Wenqi surname: Cao fullname: Cao, Wenqi organization: School of Mathematics, China University of Mining and Technology – sequence: 4 givenname: Jipeng surname: Cheng fullname: Cheng, Jipeng email: chengjp@cumt.edu.cn, chengjipeng1983@163.com organization: School of Mathematics, China University of Mining and Technology, Jiangsu Center for Applied Mathematics (CUMT) |
| BookMark | eNp9kMFKw0AQhhepYFt9AU8LnqM7O5smOWqwViwoqOdlm8zalDZbdxOwb-_WCN5kDgPD__0D34SNWtcSY5cgrkGI7CYIgSgTIdMEBBQiwRM2BhVPoGbZiI1FgXmSF5k6Y5MQNkJAlqIcs7ul-eJz53f91nSNa7mzHJPS7fbxQdvxpxe-aMgbX60PfHXgr-vGdYaXrg2d76sjcs5OrdkGuvjdU_Y-v38rF8ny-eGxvF0mlcxkl0ChCIhUXqdCoq1zAaZAg1BTRUgoLeDKxKlmxYootbWiStjCgiSZgsEpuxp699599hQ6vXG9b-NLjRJBqhyViik5pCrvQvBk9d43O-MPGoQ-utKDKx1d6R9XGiOEAxRiuP0g_1f9D_UNWG9tzQ |
| Cites_doi | 10.1143/PTPS.94.210 10.1007/BF00312674 10.1017/CBO9780511535024 10.1088/0305-4470/39/30/003 10.1063/1.533104 10.1007/s11005-017-1006-3 10.1143/JPSJ.50.3806 10.1017/9781108610902 10.1007/BF02098018 10.1088/0266-5611/10/2/001 10.1063/1.1590055 10.1142/5108 10.1007/s11005-024-01888-8 10.1090/pspum/049.1/1013133 10.1016/j.aim.2019.05.030 10.1090/crmp/014/13 10.1063/1.529875 10.2977/prims/1195182017 10.2977/prims/1195183297 10.1007/s002200050609 10.1007/s00220-020-03817-x 10.1007/s00029-021-00646-1 |
| ContentType | Journal Article |
| Copyright | The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025 Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025. |
| Copyright_xml | – notice: The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025 Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. – notice: The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025. |
| DBID | AAYXX CITATION |
| DOI | 10.1007/s00332-025-10190-3 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Mathematics |
| EISSN | 1432-1467 |
| ExternalDocumentID | 10_1007_s00332_025_10190_3 |
| GrantInformation_xml | – fundername: Qinglan Project of Jiangsu Province of China funderid: http://dx.doi.org/10.13039/501100013088 – fundername: National Natural Science Foundation of China grantid: 12171472; 12171472; 12171472; 12171472 |
| GroupedDBID | -~C -~X .86 .VR 06D 0R~ 0VY 199 1N0 203 29L 2J2 2JN 2JY 2KG 2KM 2LR 2~H 30V 4.4 406 408 409 40D 40E 5GY 5VS 67Z 6NX 78A 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AAPKM AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYZH ABAKF ABBBX ABBRH ABBXA ABDBE ABDBF ABDZT ABECU ABFSG ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABLJU ABMNI ABMQK ABNWP ABQBU ABRTQ ABSXP ABTEG ABTHY ABTKH ABTMW ABWNU ABXPI ACAOD ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSTC ACUHS ACZOJ ADHHG ADHIR ADIMF ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEFQL AEGAL AEGNC AEJHL AEJRE AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AEZWR AFBBN AFDZB AFHIU AFLOW AFOHR AFQWF AFWTZ AFZKB AGAYW AGDGC AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHPBZ AHSBF AHWEU AHYZX AIAKS AIGIU AIIXL AILAN AITGF AIXLP AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG ATHPR AVWKF AXYYD AYFIA AYJHY AZFZN B-. BA0 BAPOH BGNMA BSONS CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 EAP EBLON EBS EIOEI ESBYG EST ESX FEDTE FERAY FFXSO FIGPU FNLPD FRRFC FWDCC GGCAI GGRSB GJIRD GNWQR GQ7 GQ8 GXS HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV LAS LLZTM M4Y MA- N9A NB0 NPVJJ NQJWS NU0 O93 O9G O9I O9J OAM P19 P2P P9R PF0 PT4 PT5 QOK QOS R89 R9I RHV RNS ROL RPX RSV S16 S1Z S27 S3B SAP SDD SDH SDM SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TN5 TSG TSK TSV TUC U2A UG4 UOJIU UTJUX VC2 W23 W48 WK8 YLTOR Z45 ZMTXR ~EX -Y2 1SB 2P1 2VQ 5QI AARHV AAYTO AAYXX ABQSL ABULA ACBXY ADHKG AEBTG AEFIE AEKMD AFEXP AFGCZ AGGDS AGQPQ AJBLW AMVHM B0M BBWZM BDATZ CAG CITATION COF EAD EJD EMK EPL FINBP FSGXE H13 HZ~ I-F KOW N2Q NDZJH O9- R4E RIG RNI RZK S26 S28 SCLPG T16 TUS UZXMN VFIZW VOH ZWQNP ~8M |
| ID | FETCH-LOGICAL-c272t-194e1ee48d5023fd801a93a31dece3e32f13bababc69bee5fd4ec0f9f12e251a3 |
| IEDL.DBID | U2A |
| ISSN | 0938-8974 |
| IngestDate | Sat Aug 23 13:02:27 EDT 2025 Thu Jul 24 01:57:25 EDT 2025 Fri Jul 18 01:10:33 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 5 |
| Keywords | Tau function 3-Component KP Lax equation 35Q53 35Q51 37K10 Bilinear equation |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c272t-194e1ee48d5023fd801a93a31dece3e32f13bababc69bee5fd4ec0f9f12e251a3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 3231248344 |
| PQPubID | 2043730 |
| ParticipantIDs | proquest_journals_3231248344 crossref_primary_10_1007_s00332_025_10190_3 springer_journals_10_1007_s00332_025_10190_3 |
| PublicationCentury | 2000 |
| PublicationDate | 2025-10-01 |
| PublicationDateYYYYMMDD | 2025-10-01 |
| PublicationDate_xml | – month: 10 year: 2025 text: 2025-10-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | Journal of nonlinear science |
| PublicationTitleAbbrev | J Nonlinear Sci |
| PublicationYear | 2025 |
| Publisher | Springer US Springer Nature B.V |
| Publisher_xml | – name: Springer US – name: Springer Nature B.V |
| References | Y Cheng (10190_CR5) 1992; 33 Y Cheng (10190_CR6) 1994; 10 B Dubrovin (10190_CR12) 2019; 351 10190_CR13 J Cheng (10190_CR7) 2021; 27 J Harnad (10190_CR14) 2021 10190_CR10 10190_CR17 SQ Liu (10190_CR22) 2021; 775 V Kac (10190_CR16) 1996; 37 SQ Liu (10190_CR21) 2018; 108 Y Ohta (10190_CR25) 1988; 94 V Kac (10190_CR19) 2023; 64 W Oevel (10190_CR24) 1993; 157 M Jimbo (10190_CR15) 1983; 19 E Date (10190_CR9) 1982; 18 10190_CR20 L Dickey (10190_CR11) 2003 V Kac (10190_CR18) 2003; 44 E Date (10190_CR8) 1981; 50 10190_CR28 10190_CR27 10190_CR26 10190_CR29 T Miwa (10190_CR23) 2000 S Carpentier (10190_CR4) 2020; 380 M Adler (10190_CR1) 1999; 203 O Babelon (10190_CR2) 2003 G Carlet (10190_CR3) 2006; 39 |
| References_xml | – volume: 94 start-page: 210 year: 1988 ident: 10190_CR25 publication-title: Progr. Theor. Phys. Suppl. doi: 10.1143/PTPS.94.210 – volume: 37 start-page: 435 year: 1996 ident: 10190_CR16 publication-title: Lett. Math. Phys. doi: 10.1007/BF00312674 – volume-title: Introduction to Classical Integrable Systems year: 2003 ident: 10190_CR2 doi: 10.1017/CBO9780511535024 – volume: 64 year: 2023 ident: 10190_CR19 publication-title: J. Math. Phys. – ident: 10190_CR27 – volume: 39 start-page: 9411 year: 2006 ident: 10190_CR3 publication-title: J. Phys. A doi: 10.1088/0305-4470/39/30/003 – ident: 10190_CR29 doi: 10.1063/1.533104 – volume: 108 start-page: 261 year: 2018 ident: 10190_CR21 publication-title: Lett. Math. Phys. doi: 10.1007/s11005-017-1006-3 – volume: 50 start-page: 3806 year: 1981 ident: 10190_CR8 publication-title: J. Phys. Soc. Jpn. doi: 10.1143/JPSJ.50.3806 – ident: 10190_CR10 – volume-title: Tau Functions and Their Applications year: 2021 ident: 10190_CR14 doi: 10.1017/9781108610902 – volume: 157 start-page: 51 year: 1993 ident: 10190_CR24 publication-title: Commun. Math. Phys. doi: 10.1007/BF02098018 – volume: 10 start-page: L11 year: 1994 ident: 10190_CR6 publication-title: Inverse Probl. doi: 10.1088/0266-5611/10/2/001 – volume: 44 start-page: 3245 year: 2003 ident: 10190_CR18 publication-title: J. Math. Phys. doi: 10.1063/1.1590055 – volume-title: Soliton Equations and Hamiltonian Systems year: 2003 ident: 10190_CR11 doi: 10.1142/5108 – ident: 10190_CR13 doi: 10.1007/s11005-024-01888-8 – volume-title: Solitons: Differential Equations, Symmetries and Infinite-Dimensional Algebras year: 2000 ident: 10190_CR23 – ident: 10190_CR20 doi: 10.1090/pspum/049.1/1013133 – volume: 351 start-page: 897 year: 2019 ident: 10190_CR12 publication-title: Adv. Math. doi: 10.1016/j.aim.2019.05.030 – ident: 10190_CR17 doi: 10.1090/crmp/014/13 – ident: 10190_CR26 – volume: 33 start-page: 3774 year: 1992 ident: 10190_CR5 publication-title: J. Math. Phys. doi: 10.1063/1.529875 – volume: 19 start-page: 943 year: 1983 ident: 10190_CR15 publication-title: Publ. Res. Inst. Math. Sci. doi: 10.2977/prims/1195182017 – volume: 775 start-page: 259 year: 2021 ident: 10190_CR22 publication-title: J. Reine Angew. Math. – ident: 10190_CR28 – volume: 18 start-page: 1077 year: 1982 ident: 10190_CR9 publication-title: Publ. Res. Inst. Math. Sci. doi: 10.2977/prims/1195183297 – volume: 203 start-page: 185 year: 1999 ident: 10190_CR1 publication-title: Commun. Math. Phys. doi: 10.1007/s002200050609 – volume: 380 start-page: 655 year: 2020 ident: 10190_CR4 publication-title: Commun. Math. Phys. doi: 10.1007/s00220-020-03817-x – volume: 27 start-page: 1 year: 2021 ident: 10190_CR7 publication-title: Selecta Math. doi: 10.1007/s00029-021-00646-1 |
| SSID | ssj0017532 |
| Score | 2.39466 |
| Snippet | It is quite basic in integrable systems to derive Lax equations from bilinear equations. For multi-component KP theory, corresponding Lax structures are mainly... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Index Database Publisher |
| SubjectTerms | Analysis Classical Mechanics Differential equations Economic Theory/Quantitative Economics/Mathematical Methods Finite differences Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Operators (mathematics) Theoretical |
| Title | Lax Formulation of 3-Component KP Hierarchy by Shiota Construction |
| URI | https://link.springer.com/article/10.1007/s00332-025-10190-3 https://www.proquest.com/docview/3231248344 |
| Volume | 35 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3PT8IwFH5RuOjBH6gRRdKDN21C126sRzBMIkJMlARPS9e1gQuYjIP8976ObUSjB7PDDmtelq99fd_2-r0HcMt8JZHaJ1RzLqiQPKBKa6fkksImNpUsdQLn8SQYTsXTzJ8VorCsPO1epiTznboSu7m2Yx517VdZLoDm-1D33bc7ruKp16tyB0jA89yBRFcOkS4XUpnfbXwPRzuO-SMtmkeb6ASOCppIett5PYU9s2zAcUEZSeGQWQMOx1XZ1ewM-s_qk0TIQoueXGRlCafO5VdLDC5k9EKGC6c41vMNSTbkdb5YrRVxTTvLMrLnMI0Gbw9DWjRJoNrremvKpDDMGBGmPoZfm2LEUZIrzlKjDTfcs4wnCi8dyMQY36bC6I6VlnkGuY3iF1Bb4ktcAtHdrhsSmjSUQjOR-DoMlAnRjka7tgl3JVbxx7YWRlxVPc6RjRHZOEc25k1olXDGhV9kMUc66bn_l6IJ9yXEu8d_W7v63_BrOPC2s0w7rAU1BNHcIHtYJ22o96J-f-Luj--jQTtfPF9BRL4f |
| linkProvider | Springer Nature |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV09T8MwED1BGYCBjwKiUMADG1jCsZPGY0FUgX4IiVbqFjmOrXZpkdKB_nvOqdMKBAPKGOsUPefynnJ-dwC3LFQSpX1GNeeCCskjqrR2Ti4pbGZzyXJncO4PomQkXsfh2JvCiuq0e1WSLL_Ua7ObGzsWUDd-lZUGaL4NOygGYneQaxS017UDFOBl7UBiKscol71V5vcY3-loozF_lEVLtukcwYGXiaS92tdj2DKzOhx6yUh8QhZ12O-v264WJ_DYU5-kgyrUz-Qic0s4dSk_nyG5kO4bSabOcawnS5ItyftkOl8o4oZ2Vm1kT2HUeR4-JdQPSaA6aAULyqQwzBgR5yHSr82RcZTkirPcaMMNDyzjmcJLRzIzJrS5MPrBSssCg9pG8TOozfAhzoHoVsstiU0eS6GZyEIdR8rEGEdjXNuAuwqr9GPVCyNddz0ukU0R2bRENuUNaFZwpj4vipSjnAzc_0vRgPsK4s3tv6Nd_G_5Dewmw34v7b0MupewF6x2nD6wJtQQUHOFSmKRXZcvzhdxGb4C |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV07T8MwED5BkRAMPAqIQgEPbGC1jp00HssjKvShSlCpW-Q4ttqlrdQO9N9zTpMWEAwoY6yT89nn-5Tzdwdwy3wlkdonVHMuqJA8oEprp-SSwiY2lSx1AuduL2gNxOvQH35R8We33YuU5ErT4Ko0TRa1WWpra-Gba0HmUdeKlWViaL4NO3gcM7evB15znUdAMp7lESS6dYjUOZfN_G7je2ja8M0fKdIs8kRHcJBTRtJcrfExbJlJGQ5z-khy55yXYb-7LsE6P4GHjvogETLSvD8XmVrCqXP_6QQ_lLT7pDV26mM9WpJkSd5G4-lCEdfAsygpewqD6Pn9sUXzhglUew1vQZkUhhkjwtTHUGxTjD5KcsVZarThhnuW8UThowOZGOPbVBhdt9IyzyDPUfwMShOcxDkQ3Wi4IaFJQyk0E4mvw0CZEO1otGsrcFdgFc9WdTHidQXkDNkYkY0zZGNegWoBZ5z7yDzmSC099y9TVOC-gHjz-m9rF_8bfgO7_aco7rz02pew560WnNZZFUqIp7lCUrFIrrN98wnFjsI- |
| 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=Lax+Formulation+of+3-Component+KP+Hierarchy+by+Shiota+Construction&rft.jtitle=Journal+of+nonlinear+science&rft.au=Cui%2C+Tongtong&rft.au=Wang%2C+Jinbiao&rft.au=Cao%2C+Wenqi&rft.au=Cheng%2C+Jipeng&rft.date=2025-10-01&rft.issn=0938-8974&rft.eissn=1432-1467&rft.volume=35&rft.issue=5&rft_id=info:doi/10.1007%2Fs00332-025-10190-3&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s00332_025_10190_3 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0938-8974&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0938-8974&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0938-8974&client=summon |