Solutions of a nonlinear eigenvalue problem.

What is it about?

The eigenvalues and eigenfunctions of a differential algebraic eigenvalue problem are calculated essentially explicitly. Specifically, the problem is discretized by looking for solutions in the form of series (Fourier or Dirichlet).

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Why is it important?

This is an example of a nonlinear oscillator. Just as a linear oscillator (RLC circuit) leads to the Fourier transform, this one leads to a generalized Fourier transform. It is demonstrated in subsequent publications that such transforms, while non-orthogonal, admit useful novel applications, e.g. they underpin a noise vanishing phenomenon (the broadband redundancy). The discrete versions of such transforms can be implemented via fast algorithms. Also, the eigenvalue problem considered here is an example of a model of an RLCM circuit, where M stands for memristance. Memristance is a feature of nano-electronic circuits. The techniques developed in this paper apply to a plethora of other examples.

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