Kudryashov and Sinelshchikov’s method for solving the radial oscillation problem of multielectron bubbles in liquid helium
This work investigates the exact general analytical solution of the Rayleigh equation for multielectron bubbles in liquid helium using Kudryashov and Sinelshchikov’s method. We firstly obtain its first integral involving three negative exponential powers, then a specific Sundman transformation is pr...
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| Veröffentlicht in: | Journal of mathematical chemistry 2020-08, Vol.58 (7), p.1481-1488 |
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| container_end_page | 1488 |
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| container_issue | 7 |
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| container_title | Journal of mathematical chemistry |
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| creator | Qin, Yupeng Lou, Qingjun Wang, Zhen Zou, Li |
| description | This work investigates the exact general analytical solution of the Rayleigh equation for multielectron bubbles in liquid helium using Kudryashov and Sinelshchikov’s method. We firstly obtain its first integral involving three negative exponential powers, then a specific Sundman transformation is proper established to transform it into an equation for the elliptic functions, and finally the analytical solution expressed by Weierstrass elliptic function is constructed appropriately. As applications, the derived analytical solution is used to test numerical algorithm, and also to construct the analytical expressions of the bubble oscillation period and the derivatives of the bubble radius. Further, the influence of the pressure on the helium is also discussed. |
| doi_str_mv | 10.1007/s10910-020-01145-y |
| format | Article |
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We firstly obtain its first integral involving three negative exponential powers, then a specific Sundman transformation is proper established to transform it into an equation for the elliptic functions, and finally the analytical solution expressed by Weierstrass elliptic function is constructed appropriately. As applications, the derived analytical solution is used to test numerical algorithm, and also to construct the analytical expressions of the bubble oscillation period and the derivatives of the bubble radius. Further, the influence of the pressure on the helium is also discussed.</description><identifier>ISSN: 0259-9791</identifier><identifier>EISSN: 1572-8897</identifier><identifier>DOI: 10.1007/s10910-020-01145-y</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Algorithms ; Bubbles ; Chemistry ; Chemistry and Materials Science ; Elliptic functions ; Exact solutions ; Helium ; Liquid helium ; Math. 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We firstly obtain its first integral involving three negative exponential powers, then a specific Sundman transformation is proper established to transform it into an equation for the elliptic functions, and finally the analytical solution expressed by Weierstrass elliptic function is constructed appropriately. As applications, the derived analytical solution is used to test numerical algorithm, and also to construct the analytical expressions of the bubble oscillation period and the derivatives of the bubble radius. Further, the influence of the pressure on the helium is also discussed.</description><subject>Algorithms</subject><subject>Bubbles</subject><subject>Chemistry</subject><subject>Chemistry and Materials Science</subject><subject>Elliptic functions</subject><subject>Exact solutions</subject><subject>Helium</subject><subject>Liquid helium</subject><subject>Math. Applications in Chemistry</subject><subject>Mathematical analysis</subject><subject>Numerical analysis</subject><subject>Original Paper</subject><subject>Physical Chemistry</subject><subject>Rayleigh equations</subject><subject>Theoretical and Computational Chemistry</subject><issn>0259-9791</issn><issn>1572-8897</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kMtKxDAUhoMoOI6-gKuA62ouvSRLEW844EJdhzRNphnTZiZpBwoufA1fzycxOoI7F4ez-C_n8AFwitE5Rqi6iBhxjDJE0mCcF9m0B2a4qEjGGK_2wQyRgme84vgQHMW4QghxVrIZeHsYmzDJ2PotlH0Dn2yvXWxVa1_99vP9I8JOD61voPEBRu-2tl_CodUwyMZKB31U1jk5WN_DdfC10x30BnajG6x2Wg0hCfVYJyFC20NnN6NtYKudHbtjcGCki_rkd8_By83189Vdtni8vb-6XGSKYj5kBtellKqi1DCNck2qmjSaSUkN5aUq8tpw0-Qqr5iWHBNGcmlYUyYyNcOK0Tk42_WmDzejjoNY-TH06aQgOcEFpimTXGTnUsHHGLQR62A7GSaBkfimLHaURaIsfiiLKYXoLhSTuV_q8Ff9T-oLVg6EmA</recordid><startdate>20200801</startdate><enddate>20200801</enddate><creator>Qin, Yupeng</creator><creator>Lou, Qingjun</creator><creator>Wang, Zhen</creator><creator>Zou, Li</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-4874-7579</orcidid></search><sort><creationdate>20200801</creationdate><title>Kudryashov and Sinelshchikov’s method for solving the radial oscillation problem of multielectron bubbles in liquid helium</title><author>Qin, Yupeng ; Lou, Qingjun ; Wang, Zhen ; Zou, Li</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-f1b6aac733f8e04e27b2de8aa3f396c54bf9fd4c478ea912824af8d6100b81c83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Algorithms</topic><topic>Bubbles</topic><topic>Chemistry</topic><topic>Chemistry and Materials Science</topic><topic>Elliptic functions</topic><topic>Exact solutions</topic><topic>Helium</topic><topic>Liquid helium</topic><topic>Math. Applications in Chemistry</topic><topic>Mathematical analysis</topic><topic>Numerical analysis</topic><topic>Original Paper</topic><topic>Physical Chemistry</topic><topic>Rayleigh equations</topic><topic>Theoretical and Computational Chemistry</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Qin, Yupeng</creatorcontrib><creatorcontrib>Lou, Qingjun</creatorcontrib><creatorcontrib>Wang, Zhen</creatorcontrib><creatorcontrib>Zou, Li</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of mathematical chemistry</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Qin, Yupeng</au><au>Lou, Qingjun</au><au>Wang, Zhen</au><au>Zou, Li</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Kudryashov and Sinelshchikov’s method for solving the radial oscillation problem of multielectron bubbles in liquid helium</atitle><jtitle>Journal of mathematical chemistry</jtitle><stitle>J Math Chem</stitle><date>2020-08-01</date><risdate>2020</risdate><volume>58</volume><issue>7</issue><spage>1481</spage><epage>1488</epage><pages>1481-1488</pages><issn>0259-9791</issn><eissn>1572-8897</eissn><abstract>This work investigates the exact general analytical solution of the Rayleigh equation for multielectron bubbles in liquid helium using Kudryashov and Sinelshchikov’s method. 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| subjects | Algorithms Bubbles Chemistry Chemistry and Materials Science Elliptic functions Exact solutions Helium Liquid helium Math. Applications in Chemistry Mathematical analysis Numerical analysis Original Paper Physical Chemistry Rayleigh equations Theoretical and Computational Chemistry |
| title | Kudryashov and Sinelshchikov’s method for solving the radial oscillation problem of multielectron bubbles in liquid helium |
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