# 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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### No even-order harmonics in alkali gases? (Intuition for “symmetry in time domain'')

The polarizability can be expanded in the from: In Alkali gases, it is said that $\chi^3$ can be nonzero, and the combination of multiple waves can produce four-wave-mixing. But what about $\chi^2$? ...
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### Does QED evolve unitarily after the Schwinger limit?

If QED becomes nonlinear after the Schwinger limit, shouldn't QED no longer be unitary (above the limit) since linearity is a requirement of a unitary operator (and vice versa)? Does this mean that ...
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### Applications or work that has been done in Non-Linear dynamics or Chaos

I have almost finished my Non-Linear Dynamics course. I'm really interested in working on this field but first I want to see and study some of the work or application that has already been done in ...
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### Electric field of a capacitor with a non-linear dielectric

Let's consider a parallel plate capacitor with a non-linear dielectric: The electric field between the plates will be equal to: $$E = V/d$$ where d is the distance and V the voltage between the ...
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### Dynamical system fixed point by perturbation?

Suppose I have an non-linear autonomous system : $$\dot{x}_i(t) = f(x_i(t)) + \lambda g(x_i(t))$$ I am interested in finding its fixed points. I want to know if the following method of ...
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### When can complex real world phenomena be modeled as simple low dimensional systems?

My main interests are biological systems, but the question is general. I was trained in computational biology, and virtually all quantitative models of biological processes I've encountered in my ...
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### Why is Newton's second law with potentials not a linear equations?

I was trying to learn Quantum physics by myself using MIT's 8.04 course. I came accross this equation: I don't understand why the above is true. I understand the definition of linearity. But I don't ...
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### Resistive forces on Simple Harmonic motion

How is a simple harmonic motion affected by resistive forces? In this case, a spring block system is placed on rough horizontal surface. How to derive the block's displacement equation? I couldn't ...
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### Are all familiar symmetry transformations, when they act on fields, linear? [duplicate]

Consider symmetry transformation acting on a field or a set of fields. For example, a gauge transformation of the form $$\phi^\prime_a(x)=U_{ab}(x)\phi_b(x)$$ where $U(x)$ is a matrix with elements ...
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### Why would we want to calculate the Lyapunov exponent for experimental data?

Searching Google Scholar for "Lyapunov exponent from time series" turns up multiple papers (some of them highly cited) suggesting methods for estimating the largest Lyapunov exponent or sometimes even ...
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### How are jerk equations connected to chaos theory?

I read in this Wikipedia article: It has been shown that a jerk equation, which is equivalent to a system of three first-order, ordinary non-linear differential equations, is the minimal setting ...
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### What are the necessary and sufficient conditions for a motion to be periodic?

Consider the following idealized motions (i) The motion of a bob attached to a spring on a horizontal frictionless table, (ii) the motion of a pendulum with an arbitrary amplitude without air ...
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### Physical meaning of third derivative with respect to position

I currently on a numerical solver for the KdV equation which reads $$u_t + uu_x = u_{xxx}$$ I was wondering the physical sense of this third derivative with respect to $x$. I know that the $uu_x$ ...
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### Instability of coupled non-linear oscillators

Consider a bunch of interacting oscillators (e.g., a chain of atoms), interacting due to anharmonicity in the potential energy. You can Taylor expand the force on each oscillator about equilibrium ...
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### Is the quantum dynamics of a system of interacting particles linear or non-linear?

As I understand it, the linearity of quantum mechanics is considered to be an inviolable principle - e.g., this paper - because (among other things) causality would be violated or and/or superluminal ...
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### What can one conclude about the stability of limit cycles without the use of numerical methods?

Let's assume one asserts the existence of a closed orbit by applyling the Poincaré-Bendixson theorem to a trapping region $R$ that is constructed such that all phase vectors on its boundary point ...