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We investigate the non-linear coupling between radial and non-radialoscillations of static spherically symmetric neutron stars as a possiblemechanism for the generation of gravitational waves that may lead to observablesignatures. In this paper we concentrate on the axial sector of the non-radialperturbations. By using a multi-parameter perturbative framework we introduce acomplete description of the non-linear coupling between radial and axialnon-radial oscillations; we study the gauge invariant character of theassociated perturbative variables and develop a computational scheme to evolvethe non-linear coupling perturbations in the time domain. We present results ofsimulations corresponding to different physical situations and discuss thedynamical behaviour of this non-linear coupling. Of particular interest is theoccurrence of signal amplifications in the form of resonance phenomena when afrequency associated with the radial pulsations is close to a frequencyassociated with one of the axial w-modes of the star. Finally, we mentionpossible extensions of this work and improvements towards more astrophysicallymotivated scenarios.Comment: RevTeX 4. 23 pages, 13 figure

Coupling of radial and axial nonradial oscillations of compact stars: Gravitational waves from first-order differential rotation