Math gifts

- Art Gallery -

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: \( {\displaystyle \psi _{2}(t)=C_{\psi _{2}}\cos(\omega _{0}t){\rm {sech}}(t)} \)

Undergraduate Texts in Mathematics

Graduate Texts in Mathematics

Graduate Studies in Mathematics

Mathematics Encyclopedia



Hellenica World - Scientific Library

Retrieved from ""
All text is available under the terms of the GNU Free Documentation License