Name
Title | ||
|---|---|---|
On the Jacobi last multipliers and Lagrangians for a family of Liénard-type equations. |
Abstract | ||
|---|---|---|
We study a family of the Linard-type equations, which can be transformed via the generalized Sundman transformations into a particular case of PainlevGambier equation XXVII. We show that this equation of the PainlevGambier type admits an autonomous Lagrangian, Jacobi last multiplier and first integral. As a consequence, we obtain that the corresponding family of Linard-type equations also admits a time-independent Lagrangian, Jacobi last multiplier and first integral. We also construct the general analytical and singular solutions for members of this family of Linard-type equations by virtue of the generalized Sundman transformations. To demonstrate applications of our results we consider several examples of the Linard-type equations, with a generalization of the modified Emden equation among them, and construct their autonomous Lagrangians, Jacobi last multipliers and first integral as well as their general analytical solutions. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.amc.2017.03.010 | Applied Mathematics and Computation |
Keywords | Field | DocType |
Liénard-type equations,Sundman transformations,Lagrangians,Jacobi multipliers | Mathematical optimization,Lagrangian,Jacobi method,Mathematical analysis,Multiplier (economics),Mathematics | Journal |
Volume | Issue | ISSN |
307 | C | 0096-3003 |
Citations | PageRank | References |
2 | 0.67 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dmitry I. Sinelshchikov | 1 | 37 | 8.79 |
| Nikolay A. Kudryashov | 2 | 49 | 15.72 |