# Questions tagged [non-linear-systems]

The term non-linear or nonlinear has several definitions but is generally used to describe a system that cannot be approximated by a superposition principle or perturbative approach.

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### Trying to solve 2D Toda Lattice Equation with Lax Pair Approach

I am working on this Hamiltonian: $$H = \frac{p_1^2 + p_2^2}{2m} + e^{q_2-q_1} + e^{q_2} + e^{-q_1} -3$$ Thank you for the hint that it is a modification of the Toda Lattice Equation. Let me sketch ...
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### Nonlinear stability question

I am looking for a simple example where a system is linearly unstable, but nonlinearly unstable or stable, depending on the sign of the initial perturbation. For instance, assume the linear normal ...
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### Is it physically relevant to restrict the solution of a nonlinear PDE to positive frequencies in the Fourier transfrom?

I would like to mention that I am a mathematician and not a physicist, so I apologize in advance if my question seems obvious. Considering any linear PDE, it is common to understand the behavior of ...
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### Initial value formulation of Yang-Mills equation

In Wald Chapter 10, he discusses the initial value formalism of electromagnetism - how Maxwell's equations are actually a system of three equations plus an initial value constraint, and how we can ...
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### What is the mechanism of subharmonic oscillations?

It's clear to me from linear systems theory that energy manifested within a fundamental mode of resonance can saturate with the excess energy spilling over into harmonic frequencies greater than the ...
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