English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In the present note, we address the general nonlinear oscillator of the form  q ″+ aq ′+ b ( t ) q + c ( t ) q n  =0, where  q  as well as the coefficients  b ( t ) and  c ( t ) are complex or real-valued functions of the real variable  t ;  a  is a real constant, and  n  is a real number. By starting with a certain Hamiltonian function, we discuss conditions on the functions  b ( t ) and  c ( t ) for which such differential equation becomes able to admit a nonclassical energy integral – i.e. a  t -dependent energy integral. A method to inversely elicit the corresponding conservative solutions of this differential equation is consequently established, and two examples addressing periodic conservative solutions are shown.

Nonclassical t -Dependent Energy Integral of q ″+ aq ′+ b ( t ) q + c ( t ) q n =0