Nonlocal and nonvariational extensions of Killing-type equations

Gianluca Gorni; Gaetano Zampieri

doi:10.3934/dcdss.2018042

Article Contents

2018, Volume 11, Issue 4: 675-689. Doi: 10.3934/dcdss.2018042

This issue Previous Article Symmetry analysis of a Lane-Emden-Klein-Gordon-Fock system with central symmetry Next Article A study of bifurcation parameters in travelling wave solutions of a damped forced Korteweg de Vries-Kuramoto Sivashinsky type equation

Nonlocal and nonvariational extensions of Killing-type equations

Gianluca Gorni and
Gaetano Zampieri^,

Università di Udine, Dipartimento di Scienze Matematiche, Informatiche e Fisiche, via delle Scienze 208, 33100 Udine, Italy
Università di Verona, Dipartimento di Informatica, strada Le Grazie 15, 37134 Verona, Italy

* Corresponding author: Gaetano Zampieri.
* Corresponding author: Gaetano Zampieri.

Received: October 31, 2016

Revised: April 30, 2017

Published: August 2018

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Abstract

The Killing-like equation and the inverse Noether theorem arise in connection with the search for first integrals of Lagrangian systems. We generalize the theory to include "nonlocal" constants of motion of the form $N_0+∈t N_1\, dt$ , and also to nonvariational Lagrangian systems $\frac{d}{dt}\partial_{\dot q}L-\partial_qL=Q$ . As examples we study nonlocal constants of motion for the Lane-Emden system, for the dissipative Maxwell-Bloch system and for the particle in a homogeneous potential.

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Mathematics Subject Classification: Primary: 37J15, 70H33.

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