# 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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### Non-linear QM and wave function collapse [closed]

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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### Are strong gravitational fields linear with weaker ones?

This is sort of an addendum to one of my previous questions regarding the linearity of gravity. That question was about how to determine if a metric is roughly linear but in this case I am dealing ...
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### The "small amplitude" assumption in the derivation of the wave equation for the string

I am reading about the wave equation for transverse waves in a string from the book Mathematics of wave propagation (2000) by J. Davis. On page 10, just before the derivation of the (one-dimensional) ...
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### Reformulate Einstein equations to make them linear

Is it possible to reformulate the Einstein equation in terms of a new variable, say $k_{\mu\nu}$ in terms of the metric $g_{\mu\nu}$, in order to make the Einstein equations linear in $k_{\mu\nu}$?
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### How to linearise on Lagrangian level?

Consider a Lagrangian density $$\mathcal{L}(\phi, \nabla \phi) = \frac{1}{2} \, g^{\mu \nu} \, \partial_{\mu} \phi \; \partial_{\nu} \phi + V(\phi) \tag{1}$$ The equation of motion (EOM), i.e. the ...
1 vote
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### What are some good resources to learn fluid mechanics? [duplicate]

I know that there are a lot of resources out there to be explored and I have gone through several of them. What I want is some resource where fluid mechanics is treated, from a geometric viewpoint, ...
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### What is a diabolical point?

A lot of papers define a 'diabolical point' as a "double semi-simple eigenvalue." I know a semi-simple eigenvalue is one which has algebraic multiplicity and geometric multiplicity to be equal. ...
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### Why do shockwaves refract when they travel into the ground?

If a shockwave from something like an explosion travels into the ground, why will it refract? The speed of sound is far different in the ground, but what would make it refract? I can’t seem to find ...
1 vote
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### Does every shockwave have an expansion wave behind it?

Do all shockwaves have an expansion fan or expansion wave behind them? Does the air always expand behind a shockwave? I assume that the strength of the expansion wave depends on the strength of the ...
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### How do shockwaves interact?

As seen here, there are two T-38's going supersonic. What happens when those shockwaves interact? They seem to dissipate in some places on this photo when they interact. Any source online says that ...
1 vote
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### How are shockwaves able to refract?

How are shockwaves able to refract? As said here, When two shock waves collide, they interact with each other and produce complex patterns of compression, rarefaction, and reflection. The resulting ...
1 vote
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### Dispersion relation for non-harmonic waves

This question is related to my previous one. The entire linear theory of waves is built on dispersion relations, which represent the algebraic dependence of frequency on wave number. That is we ...
1 vote
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### Validity of approach to nonlinear, driven, damped oscillation amplitudes in L&L

In §29 of L&L mechanics, the authors discuss an approach to estimate the resonance amplitude of the equation $\ddot{x}+2\lambda\dot{x}+\omega_0^2x = \frac{f}{m}\cos(\gamma t)-\alpha x^2-\beta x^3$ ...
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### Entropy in chaos dynamics

I'm curious about how entropy is defined within chaos theory. Are there analogous laws similar to the second law of thermodynamics? How do we define steady-state or equilibrium within the state space ...
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### Can protrusions on the smooth surface of a floating (or flying) body not slow it down, but accelerate it?

These protrusions are sure to create turbulent vortices. But what if these additional vortices can somehow lead to acceleration? Additional clarification It is clear that moving protrusions such as ...
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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, ...