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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13 views

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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56 views

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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136 views

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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294 views

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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51 views

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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49 views

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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264 views

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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388 views

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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12 views

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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1answer
91 views

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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1answer
139 views

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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2answers
109 views

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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39 views

Solution of Burgers' equation in preshock region

According to Hamilton's & Blackstock's Nonlinear acoustics (Section 4.5.4) the solution of Burgers' equation of the form: $$ \frac{\partial P}{\partial \sigma} - \frac{1}{\Gamma}\frac{\partial^2 ...
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40 views

What kind of damping is this $F = -ax|x'|$?

From Applied Mathematics by Logan: A mass hanging on a spring is <...> governed by $$mx'' = -ax|x'| - kx$$ where $-ax|x'|$ is a nonlinear damping force. I looked up "nonlinear damping" ...
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21 views

Stability of fix-point of a system of 3 non linear first order ODE, when one of the eigenvalues of Jacobian is zero

I have been working on a mean-field solution for am open quantum system model, to compare with the numerical solution of the exact solution. I have solved the system for steady state, but am now ...
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9 views

Is it possible to calculate the Hamiltonian for the Kuramoto model ? If yes, then how? [duplicate]

I just want to know whether the Hamiltonian for the Kuramoto model is possible or not.Also does the temperature have any affect on its synchronization or not? Thanks in advance.
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Fermi-Pasta-Ulam for the beam equation

The Fermi-Pasta-Ulam numerical experiment is based upon the discrete wave equation, with a small non-linearity added to the forcing term. Does anybody know of similar research performed on the beam ...
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18 views

Difference between Stuart Landau equation and Ginzburg Landau equation

I have to study the Ginzburg Landau equation, but I have been told to begin by a simplier equation: the Stuart Landau one. I understand that both of these equations are used to describe nonlinear ...
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3answers
337 views

How to do linear stability analysis on this system of ODEs?

I was trying to do linear stability analysis of spring pendulum. I arrived at the differential equations which describe the system. But I am unable to proceed to linear stability analysis. Is it ...
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1answer
504 views

Non-linear waves and shock formation

In the cases of non-linear acoustics, why is shock formation unlikely when the dispersion is strong when compared to the non-linearity of the wave?
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65 views

Question about a Attractors in Non-linear Systems

I've recently been reading up on non-linear dynamics and came across the concept of attractors. I'd like to ask if the concept of attractors can be used for pedestrian egress from a room? Since ...
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What's the probability distribution of a deterministic signal or how to marginalize dynamical systems?

In many signal processing calculations, the (prior) probability distribution of the theoretical signal (not the signal + noise) is required. In random signal theory, this distribution is typically a ...
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309 views

Explanation of the waves on the water planet in the movie Interstellar?

We will ignore some of the more obvious issues with the movie and assume all other things are consistent to have fun with some of these questions. Simple [hopefully] Pre-questions: 1) If the water ...
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1answer
75 views

Homoclinic orbit and a particle in a double well

The physical set-up is a classical particle in a parabolic double well: Physically, a particle with reasonable amount of potential energy would be able to roll down the slope of the well, roll past ...
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17 views

T-Symmetry and spatial symmetry of a multivariate conserved quantity

Definition: A reversible system is defined to be any second-order system that is invariant under the map. $t \mapsto -t$ $y \mapsto -y$ Suppose there exists a multivariate function $f(x,...
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31 views

Is there a Bayesian theory of deterministic signal? Prequel and motivation for my previous question

This is a prequel to my question: What's the probability distribution of a deterministic signal or how to marginalize a dynamical system? Clearly my question looks at the same time fairly ...
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1answer
59 views

Numerical construction of phase space for a dynamical system

Suppose I have a standard, deterministic dynamical system. For concreteness I'll assume it's a two variable system of the form, $$ \dot x_1 = f(x_1,x_2; \theta_1)\\ \dot x_2 = g(x_1,x_2; \theta_2) $$ ...
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96 views

Meaning of Smooth Dynamical System?

What does smooth dynamical system mean? It is the title of a paper I am supposed to read in non linear systems.
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105 views

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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21 views

Is there nonlinear system have both stable and asymptotically stable equilibrium points?

A nonlinear dynamical system can have multiple equilibrium points with different characteristics. I know that a pendulum with friction model $$\dot x_1 = x_2$$ $$\dot x_2 = -\dfrac{Mgl}{I} \sin(...
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Averaging over periodic functions in the derivation of the Kuramoto model

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}...
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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?
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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 ...
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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 ...
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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 ?
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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, ...
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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 ...
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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 ...
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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. ...
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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 ...
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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 ...
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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 ...
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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 ...
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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)))...
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Chaos is predictable?

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 - ...