Solvable Cubic Resonant Systems
Weakly nonlinear analysis of resonant PDEs in recent literature has generated a number of resonant systems for slow evolution of the normal mode amplitudes that possess remarkable properties. Despite being infinite-dimensional Hamiltonian systems with cubic nonlinearities in the equations of motion,...
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| Veröffentlicht in: | Communications in mathematical physics 2019-07, Vol.369 (2), p.433-456 |
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| container_title | Communications in mathematical physics |
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| creator | Biasi, Anxo Bizoń, Piotr Evnin, Oleg |
| description | Weakly nonlinear analysis of resonant PDEs in recent literature has generated a number of resonant systems for slow evolution of the normal mode amplitudes that possess remarkable properties. Despite being infinite-dimensional Hamiltonian systems with cubic nonlinearities in the equations of motion, these resonant systems admit special analytic solutions, which furthermore display periodic perfect energy returns to the initial configurations. Here, we construct a very large class of resonant systems that shares these properties that have so far been seen in specific examples emerging from a few standard equations of mathematical physics (the Gross–Pitaevskii equation, nonlinear wave equations in Anti-de Sitter spacetime). Our analysis provides an additional conserved quantity for all of these systems, which has been previously known for the resonant system of the two-dimensional Gross–Pitaevskii equation, but not for any other cases. |
| doi_str_mv | 10.1007/s00220-019-03365-z |
| format | Article |
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Our analysis provides an additional conserved quantity for all of these systems, which has been previously known for the resonant system of the two-dimensional Gross–Pitaevskii equation, but not for any other cases.</description><subject>Classical and Quantum Gravitation</subject><subject>Complex Systems</subject><subject>Equations of motion</subject><subject>Exact solutions</subject><subject>Hamiltonian functions</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Physics</subject><subject>Nonlinear analysis</subject><subject>Nonlinear equations</subject><subject>Nonlinear systems</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Systems analysis</subject><subject>Theoretical</subject><subject>Wave equations</subject><issn>0010-3616</issn><issn>1432-0916</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp9kMFKxDAURYMoWEd_wI0F19H3kjZNljLoKAwIjq5D0iYyQ6cdk1aY-XqjFdy5eot3z71wCLlEuEGA6jYCMAYUUFHgXJT0cEQyLDijoFAckwwAgXKB4pScxbgBAMWEyMjVqm8_jW1dPh_tus5fXOw70w35ah8Ht43n5MSbNrqL3zsjbw_3r_NHunxePM3vlrTmqAbKeeOYS3uFLwtZNdJjBd54W9RCscZXElAYVfGGSWmMFaaEwiqjlLTOMsZn5Hrq3YX-Y3Rx0Jt-DF2a1OmrWCmUgJRiU6oOfYzBeb0L660Je42gv0XoSYROIvSPCH1IEJ-gmMLduwt_1f9QXwpoXzI</recordid><startdate>20190701</startdate><enddate>20190701</enddate><creator>Biasi, Anxo</creator><creator>Bizoń, Piotr</creator><creator>Evnin, Oleg</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-3523-091X</orcidid></search><sort><creationdate>20190701</creationdate><title>Solvable Cubic Resonant Systems</title><author>Biasi, Anxo ; Bizoń, Piotr ; Evnin, Oleg</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-33de2e4324f5487d8f170fafb4c692df78016a973d288aab6a504b9a998beb223</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Classical and Quantum Gravitation</topic><topic>Complex Systems</topic><topic>Equations of motion</topic><topic>Exact solutions</topic><topic>Hamiltonian functions</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Physics</topic><topic>Nonlinear analysis</topic><topic>Nonlinear equations</topic><topic>Nonlinear systems</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Physics</topic><topic>Relativity Theory</topic><topic>Systems analysis</topic><topic>Theoretical</topic><topic>Wave equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Biasi, Anxo</creatorcontrib><creatorcontrib>Bizoń, Piotr</creatorcontrib><creatorcontrib>Evnin, Oleg</creatorcontrib><collection>CrossRef</collection><jtitle>Communications in mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Biasi, Anxo</au><au>Bizoń, Piotr</au><au>Evnin, Oleg</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Solvable Cubic Resonant Systems</atitle><jtitle>Communications in mathematical physics</jtitle><stitle>Commun. 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| subjects | Classical and Quantum Gravitation Complex Systems Equations of motion Exact solutions Hamiltonian functions Mathematical analysis Mathematical and Computational Physics Mathematical Physics Nonlinear analysis Nonlinear equations Nonlinear systems Physics Physics and Astronomy Quantum Physics Relativity Theory Systems analysis Theoretical Wave equations |
| title | Solvable Cubic Resonant Systems |
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