Integration of the Classical Action for the Quartic Oscillator in 1+1 Dimensions

TL;DR

This paper derives an explicit expression for the classical action of the nonlinear quartic oscillator in 1+1 dimensions, expressed in terms of boundary data, facilitating analysis of its dynamics.

Contribution

It provides a new explicit formula for the classical action of the quartic oscillator based on extremal solutions, advancing analytical methods in nonlinear classical mechanics.

Findings

Explicit form of the classical action in terms of boundary data

Enhanced understanding of extremal solutions for the quartic oscillator

Potential applications in semiclassical and quantum analyses

Abstract

In this paper, we derive an explicit form in terms of end-point data in space-time for the classical action, i.e. integration of the Langrangian along an extremal, for the nonlinear quartic oscillator evaulated on extremals.