scholarly journals Formal Integrability for the Nonautonomous Case of the Inverse Problem of the Calculus of Variations

2012 ◽  
Author(s):  
Oana Constantinescu
Keyword(s):  
Inverse Problem ◽  
Calculus Of Variations ◽  
Formal Integrability ◽  
Nonautonomous Case

scholarly journals The inverse problem of the calculus of variations for discrete systems

2018 ◽  
Vol 51 (18) ◽  
pp. 185202 ◽  
Author(s):  
María Barbero-Liñán ◽  
Marta Farré Puiggalí ◽  
Sebastián Ferraro ◽  
David Martín de Diego
Keyword(s):  
Inverse Problem ◽  
Calculus Of Variations ◽  
Discrete Systems

Towards a geometrical understanding of Douglas's solution of the inverse problem of the calculus of variations

1994 ◽  
Vol 10 (2) ◽  
pp. 245-260 ◽  
Author(s):  
M Crampin ◽  
W Sarlet ◽  
E Martinez ◽  
G B Byrnes ◽  
G E Prince
Keyword(s):  
Inverse Problem ◽  
Calculus Of Variations

On the inverse problem of calculus of variations for fourth-order equations

2010 ◽  
Vol 466 (2120) ◽  
pp. 2309-2323 ◽  
Author(s):  
M. C. Nucci ◽  
A. M. Arthurs
Keyword(s):  
Inverse Problem ◽  
Number Theory ◽  
Calculus Of Variations ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Order Equation ◽  
Fourth Order Equation ◽  
Link Type ◽  
Even Order ◽  
Fourth Order Equations

Fels’ conditions (Fels, M. E. 1996 Trans. Amer. Math. Soc. 348 , 5007–5029. ( doi:10.1090/S0002-9947-96-01720-5 )) ensure the existence and uniqueness of the Lagrangian in the case of a fourth-order equation. We show that when Fels’ conditions are satisfied, the Lagrangian can be derived from the Jacobi last multiplier, as in the case of a second-order equation. Indeed, we prove that if a Lagrangian exists for an equation of any even order, then it can be derived from the Jacobi last multiplier. Two equations from a Number Theory paper by Hall (Hall, R. R. 2002 J. Number Theory 93 , 235–245. ( doi:10.1006/jnth.2001.2719 )), one of the second and one of the fourth order, will be used to exemplify the method. The known link between Jacobi last multiplier and Lie symmetries is also exploited. Finally, the Lagrangians of two fourth-order equations drawn from Physics are determined with the same method.

scholarly journals On the Exact Inverse Problem of the Calculus of Variations

2017 ◽  
Vol 2 (3) ◽  
Author(s):  
Veronika Chrastinová ◽  
◽  
Václav Tryhuk ◽  
Keyword(s):  
Inverse Problem ◽  
Calculus Of Variations
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