# Nonlinear resonance

**foldover effectnon-linear resonanceNonlinear Resonancesnonlinear resonant**

In physics, nonlinear resonance is the occurrence of resonance in a nonlinear system.wikipedia

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### Resonance

**resonantresonant frequencyresonance frequency**

In physics, nonlinear resonance is the occurrence of resonance in a nonlinear system. Nonlinear effects may significantly modify the shape of the resonance curves of harmonic oscillators. In nonlinear resonance the system behaviour – resonance frequencies and modes – depends on the amplitude of the oscillations, while for linear systems this is independent of amplitude.

### Anharmonicity

**anharmonicanharmonic oscillatoranharmonic oscillators**

Nonlinear effects may significantly modify the shape of the resonance curves of harmonic oscillators.

Anharmonicity also modifies the energy profile of the resonance curve, leading to interesting phenomena such as the foldover effect and superharmonic resonance.

### Wave turbulence

**turbulenceturbulentweak wave turbulence**

A graphical representation of a resonant cluster of wave components is given by the corresponding NR-diagram (nonlinear resonance diagram).

### Physics

**physicistphysicalphysicists**

In physics, nonlinear resonance is the occurrence of resonance in a nonlinear system.

### Nonlinear system

**nonlinearnon-linearnonlinear dynamics**

In physics, nonlinear resonance is the occurrence of resonance in a nonlinear system.

### Amplitude

**peak-to-peakintensityvolume**

In nonlinear resonance the system behaviour – resonance frequencies and modes – depends on the amplitude of the oscillations, while for linear systems this is independent of amplitude.

### Oscillation

**oscillatorvibrationoscillators**

In nonlinear resonance the system behaviour – resonance frequencies and modes – depends on the amplitude of the oscillations, while for linear systems this is independent of amplitude.

### Linear system

**linearlinear systemslinear theory**

In nonlinear resonance the system behaviour – resonance frequencies and modes – depends on the amplitude of the oscillations, while for linear systems this is independent of amplitude.

### Natural frequency

**natural frequencieseigen-frequencyeigenfrequency**

From the physical point of view, they are defined by whether or not external force coincides with the eigen-frequency of the system (linear and nonlinear resonance correspondingly).

### Partial differential equation

**partial differential equationsPDEPDEs**

with possibly different being eigen-frequencies of the linear part of some nonlinear partial differential equation.

### Vector (mathematics and physics)

**vectorvectorsvectorial**

Here is a vector with the integer subscripts i being indexes into Fourier harmonics – or eigenmodes – see Fourier series.

### Normal mode

**modesnormal modesmode**

In nonlinear resonance the system behaviour – resonance frequencies and modes – depends on the amplitude of the oscillations, while for linear systems this is independent of amplitude. Here is a vector with the integer subscripts i being indexes into Fourier harmonics – or eigenmodes – see Fourier series.

### Fourier series

**Fourier coefficientFourier expansionFourier coefficients**

Here is a vector with the integer subscripts i being indexes into Fourier harmonics – or eigenmodes – see Fourier series.

### Diophantine equation

**Diophantine equationsDiophantine analysisDiophantine**

Accordingly, the frequency resonance condition is equivalent to a Diophantine equation with many unknowns.

### Hilbert's tenth problem

**Hilbert's 10th problem10th10th Hilbert problem**

The problem of finding their solutions is equivalent to the Hilbert's tenth problem that is proven to be algorithmically unsolvable.

### Dispersion relation

**dispersiondispersion relationsdispersive**

### Dynamical system

**dynamical systemsdynamic systemdynamic systems**

### Manley–Rowe relations

**Manley-Rowe relationsManley–Rowe constants of motion**

### Triad

**Triad (disambiguation)Treetriads**

### Quartet

**vocal quartetjazz quartetquartets**

### Harmonic oscillator

**harmonic oscillatorsharmonic oscillationdamped harmonic oscillator**

Nonlinear effects may significantly modify the shape of the resonance curves of harmonic oscillators.

### Harmonic

**harmonicsflageoletharmonic frequencies**

These functions reveal resonance ridges, harmonic, inter modulation, and energy transfer effects in a way that allows the user to relate these terms from complex nonlinear discrete and continuous time models to the frequency domain and vice versa.

### Duffing equation

**Duffing oscillatorDuffing**