# Tagged Questions

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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### Supercontinoum lasers

In my work I've encountered the phrase "supercontinuoum (CW) laser" quite a bit. After reading the wikipedia page, I'm interested in a more theoretical introductory. I'm mostly interested in ...
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### How to popularly describe typical features of a “non-linear system”

To quote Physics.SE tag definition: 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 ...
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### No-Cloning and Uncertainty: Connections or Misconception

In chapter 9 of Scott Aaronson's book "Quantum Computing Since Democritus", he make interesting but peculiar claims relating the no-cloning theorem and the Heisenberg Uncertainty Principle (HUP). Here ...
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### Why is self-organization related to scale invariance?

A lot of books mention that Scale Invariance is a property of Self-Organized critical process, but fail to mention why. Why is Scale Invariance a property of Self-Organized process.
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### Nonlinear Saturated Schrodinger Equation in 1D- Physical Models

I'm studying the Nonlinear 1d Schrodinger equation $$i\psi _t + \psi '' + |\psi |^{2p} \psi - \epsilon |\psi | ^{2q} \psi = 0\, , \quad t>0, x\in \mathbb{R}\, ,$$ and specifically, its solitary ...
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### Studying dynamic elasticity for finite deformations

this is not a question asking for help with a problem but one asking for help where to begin serious study of elasticity, particularly that applied to dynamic systems. Most textbooks about elasticity ...
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### Phase space - Diameter of attractor

For a dynamical system, with a phase space reconstructed from single scalar measurement, how do I calculate the diameter of the attractor (such as the one shown in figure below)?
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### What is a stroboscopic map?

I have an assignment where I'm supposed to generate a "stroboscopic map" of some orbits of a dynamical system. I have a hard time finding information about exactly what this kind of map is on the ...
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### Validity of the Lyapunov exponent approximation

I was trying to get the Lyapunov exponent for some dynamical nonlinear systems and found that it is not true (as I had expected) that the distance between two trajectories with slightly different ...
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### Symbolic dynamics of a multidimensional system

Let $x_t = F(x_{t-1})$ be a discrete-time dynamical system in the chaotic regime. Starting from an initial condition $x_0$, we can generate a time series $(x_t)$ where $t =1,2,...,T$ indicates the ...
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### What explanation can we give for the generation of spiral waves in a excitable medium?

I was thinking about the reason for the generation of spiral waves (a.k.a scroll waves) like in BZ reactions and Fitzhugh-Nagumo systems. Can someone give me some explanation or references ?
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### Non-Linear Behavior of Iterated Functional Maps

The universal behavior of certain iterated nonlinear function maps (ie period doubling bifurcation route to chaos): $$x_{i+1}=f(x_i)$$ have been known since Feigenbaum: (see http://...
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### Given force as function of position, find the total energy as function of time [closed]

Given that the force for a non-linear spring connected to a mass $m$ sitting on a table is $$f(x) = -kx -ax^3,$$ Find the total energy as a function of time $E(t)$. I have no clue where to begin.
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### Attractors in Duffing equation

The Duffing equation in its full form is $$\ddot{x} + \delta \dot{x} -ax + \beta x^3 = \gamma \cos(\omega t)$$ Now for specific values of the parameters several attractors exist (or not). Let's ...
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### solutions of wave equation with cubic term

Does the following equation $$\nabla^\mu \nabla_\mu \psi + a \psi^3 = b \psi$$ where $\psi$ is a real function, $a$ and $b$ are real constants, have other solutions that extend beyond a one ...
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### integrability and area-preservation property of dynamical systems

Suppose we have a map defined on a plane, $x_{1}=f(x_{0})$, where $x \in \mathbb{R}^{2}$. Assume it is integable: there exists a function $I$ of the phase space variable $x$ such that $I(x)=I(f(x))$. ...
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### Analytic proof that Lyapunov exponents in Hamiltonian systems pairwise sum to zero

I have read that in Hamiltonian systems, Lyapunov exponents come in pairs $(\lambda_i, \lambda_{2N-i+1})$ such that their sum is equal to zero. Is there a way of proving this analytically? EDIT: ...
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### What is input to state stability practically speaking

I am styuding non linear systems control and went through the input to state stability definition.Unfortunately, all I could find was some mathematical definitions. Can somebody help me to understand ...
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### Second harmonic generation - how does SHG spectrum and pulse differ from the fundamental?

I'm trying to learn about second harmonic generation (SHG) in nonlinear optics but can't seem to find a conclusive answer to the following questions. 1) If generating SHG using a pulsed laser source, ...
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### Why do spiral waves annihilate each other when 2 wavefronts collide?

I was reading about Fitzhugh-Nagumo model. And in a 2D space the simulations a Reaction-Diffusion process associated with FitzHugh system look like this. But intuitively I could not satisfy myself ...
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### In reaction-diffusion processes what is the difference between oscillatory media and excitable media?

What is the basic differences between oscillatory media and excitable media? I know that both comes under reaction-diffusion processes. Where do Turing patterns come in the picture? Can some one give ...