Modified Morlet wavelet
Encyclopedia
Modified Mexican hat, Modified Morlet and Dark soliton or Darklet wavelets are derived from hyperbolic
(sech) (bright soliton) and hyperbolic tangent (tanh) (dark soliton) pulses. These functions are derived intuitively from the solutions of the nonlinear Schrödinger equation
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:
Hyperbolic function
In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions. The basic hyperbolic functions are the hyperbolic sine "sinh" , and the hyperbolic cosine "cosh" , from which are derived the hyperbolic tangent "tanh" and so on.Just as the points form a...
(sech) (bright soliton) and hyperbolic tangent (tanh) (dark soliton) pulses. These functions are derived intuitively from the solutions of the nonlinear Schrödinger equation
Schrödinger equation
The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....
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: