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We derive fourth post-Newtonian (4PN) contributions to the Keplerian-typeparametric solution associated with the conservative dynamics of eccentric,non-spinning compact binaries. The solution has been computed while ignoringcertain zero-average, oscillatory terms arising due to 4PN tail effects. Weprovide explicit expressions for the parametric solution and various orbitalelements in terms of the conserved energy, angular momentum and symmetric massratio. Canonical perturbation theory (along with the technique of Padeapproximant) is used to incorporate the 4PN nonlocal-in-time tail effectswithin the action-angles framework. We then employ the resulting solution toobtain an updated inspiral-merger-ringdown (IMR) waveform that models thecoalescence of non-spinning, moderately eccentric black hole binaries,influenced by arXiv:1709.02007. Our updated waveform is expected to be validover similar parameter range as the above reference. We also present a relatedwaveform which makes use of only the post-Newtonian equations and thus is validonly for the inspiral stage. This waveform is expected to work for a muchlarger range of eccentricity ($e_t \lesssim 0.85$) than our full IMR waveform(which assumes circularization of the binaries close to merger). We finallypursue preliminary data analysis studies to probe the importance of includingthe 4PN contributions to the binary dynamics while constructing gravitationalwaveform templates for eccentric mergers.

Generalized quasi-Keplerian solution for eccentric, non-spinning compact binaries at 4PN order and the associated IMR waveform