Solitons
 

'Nonlinear Schrodinger equation'(NLSE) is given as

j*(du/dt) + j*u + (d^u/dx^2) + |u|^2*u = 0

The initial condition is a pulse applied at x = 0.

I want to know how to solve the NLSE to obtain the solitary waves.

(i) Either in real or spectral plane. (ii) I dont understand Split-step method and pseudo-spectral method. It'll be nice if you could suggest me a good book for these two methods. (ii) Do you think any other method could be used ?