The virial theorem for nonlinear problems

TL;DR

This paper demonstrates that the virial theorem is an effective and simple method for approximating solutions to nonlinear problems, including oscillators and bifurcation issues, offering a practical alternative to more complex methods.

Contribution

It introduces the virial theorem as a straightforward tool for analyzing nonlinear problems, aligning with previous results from Chebyshev polynomial expansions.

Findings

Virial theorem effectively approximates nonlinear oscillators.

The method applies to bifurcation problems.

Results agree with established Chebyshev polynomial methods.

Abstract

We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular we consider conservative nonlinear oscillators and a bifurcation problem. In the former case we obtain the same main result derived earlier from the expansion in Chebyshev polynomials.