# 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.

66 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
0answers
187 views

### 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 ...
1answer
391 views

### 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 ...
1answer
141 views

### Pink noise in low-dimensional systems

Pink noise (1/f) is often cited as a signature of complex or critical systems. Is it possible for a low-dimensional time-independent first-order system to generate pink noise? Intuitively it seems ...
0answers
360 views

0answers
259 views

### Exact solution for non-linear Fokker-Planck equation

I'm searching for exact (analytical) results for FP equation in 2 variables (such as $x$ and $p$ in 1D) with a steady state. Kramer's like (with force due to confining potential, such as harmonic ...
0answers
42 views

### How to use Belinsky-Zakharov transformation

I know it might be trivial. When using BZ transformation  to generate soliton solutions of Einstein’s field equations, one need a seed solution $g_{0}$ which gives $A_{0}$ and $B_{0}$. Taking them ...
0answers
142 views

0answers
34 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 ...
0answers
82 views

### 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 ...
0answers
38 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 dynamical systems? Clearly my question looks at the same time fairly ...
0answers
154 views

### 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 ...
0answers
91 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 ...
0answers
83 views

### 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://...
1answer
51 views

### 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 ...
0answers
236 views

### Lagrangian of non-linear 3 mass, 2 spring system

Given 3 masses connected by 2 springs with the angle of intersection constant, but the springs themselves bending. Young's modulus, which is a variation of Hook's Law, applies to the flexing that ...
0answers
93 views

### Generalized long wave and KdV equation

I have read many papers about benjamin-bona-mahony (BBM) equation or Regularized Long Wave (RLW) equation and found that BBM equation can be derived from KdV equation. from other papers i got others ...
0answers
30 views

### Change of variables to apply Melnikov method

Supposing there is a system of non-autonomous non-linear differential equations with small damping and small forcing. The unperturbed system (zero damping and forcing) is Hamiltonian but neither has a ...
1answer
72 views

### Tangent and Normal accelerations position estimation

How can I derive a particle position given it's last known positions (x,y), velocities in it's components (vx, vy), tangential and centripetal (normal) accelerations? (this is the only available data) ...
0answers
267 views

### Hysteresis in the Lorenz Equations

I was going through Strogatz's wonderful book on nonlinear dynamics and while reading through one problem he posed at the end of the chapter, I did not really understand what was going on. So I hope ...
0answers
48 views

### Data Collection of oscillatory motion

I'd like to study nonlinear oscillatory motion this semester. I plan to build several different mechanical systems (pendula, masses on springs, etc with and without driving forces, large/ small drag, ...
0answers
77 views

0answers
22 views

### Distinguishing a LTI from not with unknown inputs

Linear time invariant (LTI) systems are a staple of physics. They appear in many situations. But how do you know a system is a LTI? In particular, if you are provided with a black box which ...