# 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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### 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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### Why does the non-linearity of the string action prohibit stretching due to strong excitations?

From 't Hooft's String Theory lecture notes on page 8 (paraphrased): To understand hadronic particles as excited states of strings, we have to study the dynamical properties of these strings, and ...
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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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### How to simulate pendulum movement with high amplitude

I need to make a C# simulator for a simple pendulum. I have been searching the web for 3 days and I am stuck. The problem is I have found many equations that would give the angle position as a ...
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### Non linear QM and wave function collapse

I heard that there have been some propositions about describing the collapse of the wave-function by adding non-linear terms, but I couldn't anything in any any textbooks or even articles (probably ...
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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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### Failure of Superposition principle at high amplitudes

Why does superposition principle fail at high amplitudes. Please answer with respect to transverse waves. If possible, plane progressive transverse waves at best.
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### Does Lyapunov exponent equate to exponential inflation?

Physics can be modeled by dynamical systems $f^t(x)$ as well as by PDEs. The most common dynamical system has hyperbolic fixed point and can be an attractor or a repellor. The dynamics at repellors ...
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### Viscous Burgers equation physical meaning

The viscous Burgers' equation: $$q_{t}+q\:q_{x}~=~\nu\:q_{xx}, \mbox{ where } \:\:\nu >0,$$ combines the nonlinear propagation of $q(x,t)$ and the diffusion. What is this equation for? (in ...
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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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### Turbulent spacetime from Einstein equation?

It is well known that the fluid equations (Euler equation, Navier-Stokes, ...), being non-linear, may have highly turbulent solutions. Of course, these solutions are non-analytical. The laminar flow ...
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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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### How to properly use Perturbation Theory in classical systems?

Context: If we consider a particle in upwards motion near the Earth's surface and acted by a quadratic drag we get the non-linear eom: $$\frac{dv}{dt}=-g-\frac{b}{m}v^2.$$ We can solve it ...
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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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In the book "Chemical Oscillations, Waves, and Turbulence" Kuramoto derive his phase model. In this derivation he averaged over a fast period T (on page 66): $$\Gamma(\psi_a - \psi_{a'}) = \frac{1}{T}... 2answers 61 views ### Why can some oscillations be modeled by Simple Harmonic Motion, while others cannot? For some oscillators an increase in the driving amplitude changes the period (frequency) of the oscillation, but the simple harmonic oscillator does not predict this type of behavior. Why? 0answers 30 views ### Why do vortices scatter at right-angles I have been taking a course on non-perturbative physics and currently the teacher is away so I cannot ask him. In the lectures, he made the claim that a pair of vortices in the abelian-Higgs model ... 2answers 217 views ### Why is my Lyapunov exponent similar for single and double pendulum? This is my first question here on stackexchange. I hope that I can be understood. If not, tell me and I will reformulate and fill in with details. I have simulated a single pendulum and a double ... 3answers 63 views ### 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 ? 2answers 1k views ### warp drive with gravitational waves in the nonlinear regime gravitational waves are strictly transversal (in the linear regime at least), also their amplitudes are tiny even for cosmic scale events like supernovas or binary black holes (at least far away, ... 1answer 57 views ### Poincare-Bendixson Theorem Under Time Reversal Strogatz's textbook "Nonlinear Dynamics and Chaos", Chapter 7 presents the Poincare-Bendixson theorem, which gives conditions under which one can conclude the existence of a closed orbit within some ... 0answers 27 views ### Good textbooks on nonlinear electrodynamics? Looking for suggestions for a good textbook on nonlinear electrodynamics, not going into optics immediately as most textbooks tend to do but perhaps a rigorous mathematical exposition on the ... 2answers 1k views ### Nonlinear dynamics beneath quantum mechanics? Yesterday I asked whether the Schroedinger Equation could possibly be nonlinear, after reviewing the answers and material given to me in that thread I feel like my question were adequately answered. ... 2answers 48 views ### Question about limit cycles and linear systems In here http://users.isy.liu.se/en/rt/claal20/SysBio2015/Notes_SysBio_2015_partC.pdf it says: A limit cycle is however an intrinsically nonlinear concept: a linear system cannot have a limit ... 1answer 62 views ### Wave vector relation in nonlinear material A light wave (k_1,\omega_1) travels in a medium of refractive index n_1 and then encounters a nonlinear medium (n_2) under the angle \theta_1. Snell's law tells us the wave's direction in the ... 2answers 46 views ### Why do materials show plastic behaviour for large stress? As the stress is increased, the strain increases proportionally up to elastic limit and the material regains its original dimension within elastic limit. When the stress is increased further the ... 3answers 1k views ### A good, concrete example of using “chaos theory” to solve an easily understood engineering problem? Can anyone suggest a good, concrete example of using "chaos theory" to solve an easily understood engineering problem? I'm wondering if there is a an answer of the following sort: "We have a high ... 1answer 62 views ### Do all equillibrium points of a discrete mapping show up on the bifurcation diagram? The question in the title is perhaps vaguely posed, so I'll include the concrete example which is bugging me. Suppose we have a mapping given by$$N_{t+1}=N_t\cdot \exp(r(1-N_t-PN_t/(\alpha^2+N_t^2)))...
I'm reading a book of computational physics [1] where the driven nonlinear pendulum is studied in depth. This is the equation derived in the book:  \frac{d^2\theta}{dt^2} = -\frac{g}{l}\sin\theta - ...