Dark Soliton

Modified Mexican hat, Modified Morlet and Dark soliton or Darklet wavelets are derived from

hyperbolic Hyperbolic is an adjective describing something that resembles or pertains to a hyperbola (a curve), to hyperbole (an overstatement or exaggeration), or to hyperbolic geometry. The following phenomena are described as ''hyperbolic'' because they ...

(sech) (bright soliton) and hyperbolic tangent (tanh) (dark soliton) pulses. These functions are derived intuitively from the solutions of the nonlinear

Schrödinger equation The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of th ...

in the anomalous and normal dispersion regimes in a similar fashion to the way that the Morlet and the Mexican hat are derived. The modified Morlet is defined as:

\psi_2(t)=C_\cos(\omega_0 t)(t)

Wavelets {{signal-processing-stub