Modified Morlet wavelet

Modified Mexican hat, Modified Morlet and Dark soliton or Darklet wavelets are derived from hyperbolic secant (sech) (bright soliton) and hyperbolic tangent (tanh) (dark soliton) pulses. These functions are derived intuitively from the solutions of the nonlinear Shrodinger equation in the anomalous and normal dispersion regimes in a similar fashion the Morlet and the Mexican hat are derived. The modified Morlet is defined as: $\psi _{2}(t)=C_{\psi _{2}}\cos(\omega _{0}t){\rm {sech}}(t)$