Folding transformations of equations from the Gambier family
•Using a generalized folding transformation we establish a connection between the generalized second-order Abel and Gambier equations.•As an application (dynamical) of folding transformation we find that the Darboux polynomials are invariant.•In consequence of this invariance the first integrals are...
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| Veröffentlicht in: | Communications in nonlinear science & numerical simulation 2015-05, Vol.22 (1-3), p.1028-1035 |
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| container_title | Communications in nonlinear science & numerical simulation |
| container_volume | 22 |
| creator | Guha, Partha Ghose Choudhury, A. |
| description | •Using a generalized folding transformation we establish a connection between the generalized second-order Abel and Gambier equations.•As an application (dynamical) of folding transformation we find that the Darboux polynomials are invariant.•In consequence of this invariance the first integrals are also invariant.
Using Okamoto’s folding transformation we investigate the mapping of the Gambier equation and its higher-order analogs to the generalized Abel chain of equations. In particular we show how the Darboux polynomials and first integral of the Abel equation can be mapped to an equation of the Gambier type using folding transformations. |
| doi_str_mv | 10.1016/j.cnsns.2014.09.021 |
| format | Article |
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Using Okamoto’s folding transformation we investigate the mapping of the Gambier equation and its higher-order analogs to the generalized Abel chain of equations. In particular we show how the Darboux polynomials and first integral of the Abel equation can be mapped to an equation of the Gambier type using folding transformations.</description><subject>Abel sequence of differential equations</subject><subject>Chains</subject><subject>Computer simulation</subject><subject>Folding</subject><subject>Folding transformation</subject><subject>Gambier equation</subject><subject>Integrals</subject><subject>Mathematical analysis</subject><subject>Nonlinearity</subject><subject>Polynomials</subject><subject>Transformations</subject><subject>Transformations (mathematics)</subject><issn>1007-5704</issn><issn>1878-7274</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp9kLFOwzAQhi0EEqXwBCwZWRLOiR3HEgyoogWpEgvMluOcwVUSt3aK1LfH0M5Mdyf930n_R8gthYICre83hRnjGIsSKCtAFlDSMzKjjWhyUQp2nnYAkXMB7JJcxbiBREnOZuRh6fvOjZ_ZFPQYrQ-DnpwfY-Zthrv96bDBD9n0hdlKD63DkFk9uP5wTS6s7iPenOacfCyf3xcv-fpt9bp4Wuemquopp12lAThtWM1ZU1vBLbZNxcE2rKSytLSjHE3HBCCrU0IK2XJsmalQWm2qObk7_t0Gv9tjnNTgosG-1yP6fVS0FkIy2dQiRatj1AQfY0CrtsENOhwUBfXrSm3Unyv160qBVMlVoh6PFKYW36mgisbhaLBzAc2kOu_-5X8AW4hzGw</recordid><startdate>201505</startdate><enddate>201505</enddate><creator>Guha, Partha</creator><creator>Ghose Choudhury, A.</creator><general>Elsevier B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>201505</creationdate><title>Folding transformations of equations from the Gambier family</title><author>Guha, Partha ; Ghose Choudhury, A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c336t-1d3a00518465486f75feb8350f842192f1d15ecd470e46486979b5eb4c3e9fac3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Abel sequence of differential equations</topic><topic>Chains</topic><topic>Computer simulation</topic><topic>Folding</topic><topic>Folding transformation</topic><topic>Gambier equation</topic><topic>Integrals</topic><topic>Mathematical analysis</topic><topic>Nonlinearity</topic><topic>Polynomials</topic><topic>Transformations</topic><topic>Transformations (mathematics)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Guha, Partha</creatorcontrib><creatorcontrib>Ghose Choudhury, A.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Communications in nonlinear science & numerical simulation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Guha, Partha</au><au>Ghose Choudhury, A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Folding transformations of equations from the Gambier family</atitle><jtitle>Communications in nonlinear science & numerical simulation</jtitle><date>2015-05</date><risdate>2015</risdate><volume>22</volume><issue>1-3</issue><spage>1028</spage><epage>1035</epage><pages>1028-1035</pages><issn>1007-5704</issn><eissn>1878-7274</eissn><abstract>•Using a generalized folding transformation we establish a connection between the generalized second-order Abel and Gambier equations.•As an application (dynamical) of folding transformation we find that the Darboux polynomials are invariant.•In consequence of this invariance the first integrals are also invariant.
Using Okamoto’s folding transformation we investigate the mapping of the Gambier equation and its higher-order analogs to the generalized Abel chain of equations. In particular we show how the Darboux polynomials and first integral of the Abel equation can be mapped to an equation of the Gambier type using folding transformations.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.cnsns.2014.09.021</doi><tpages>8</tpages></addata></record> |
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| issn | 1007-5704 1878-7274 |
| language | eng |
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| source | Elsevier ScienceDirect Journals Complete |
| subjects | Abel sequence of differential equations Chains Computer simulation Folding Folding transformation Gambier equation Integrals Mathematical analysis Nonlinearity Polynomials Transformations Transformations (mathematics) |
| title | Folding transformations of equations from the Gambier family |
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