Nonlinear Scrodinger equations solving in matlab

Hii Friends,

I am pretty new to matlab. Could anyone suggest me a wayt o solve the following nonlinear scrodinger equation

In this equation, the terms B1,B2, alpha, gamma can be considered as constants.

z and t are variables. i is imaginary term = sqrt(-1).

I would like to see how A evolves with z(distance) and time(t).

the intial A can be considered as a gaussian or a plane wave.

Is there any other information that is required?

Pavan

[John BG]

Hi Pavan

this is John BG ( <mailto:[e-mail] [e-mail]> )

is the red graph on the right hand side the result you plan to obtain?

. https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation

.

https://arxiv.org/ftp/quant-ph/papers/0305/0305158.pdf

this paper shows some of the waveform functions that are solutions to the 1 dimension Schroedinger equation.

[Torsten]

What is your interval of integration ?

What are your initial and boundary conditions ?

Best wishes

Torsten.

[Pavan Kumar]

Hii Torsten,

Thanks for the interest.

The boundary and initial conditions would be

z varies from 0 to 2 t varies as -6 to +6 A(0,t) = exp(-t^2) (gaussian pulse)

Is this information sufficient?

[Akira Agata]

This Nonlinear Schrodinger Equation is commonly used as a basic propagation model equation in optical fiber communication systems. In this research field, many researchers use split-step fourier method (SSFM) to numerically solve this equation.

https://en.wikipedia.org/wiki/Split-step_method

More details of this method can be found in the textbook "Nonlinear Fiber Optics" written by Dr. Agrawal. Of course, MATLAB can do it !

[Torsten]

You forgot to state the boundary conditions at t=+/-6, but by splitting your equation in real and imaginary part it should be possible to use "pdepe" for its solution.

Best wishes

Torsten.

Answer 1

[johnson wul]

Hi every one. well I have a problem in building code for numerical scheme of a linear discret equation using finite dieference method.

My eqution is

E*A(i)= P*cos(w*i)*A(i) + Q*( A(i-1) +A(i+1) ) where w,Q are fixed constants and i is interger index on the amplitud A

P=[0 : 6] . I need to plot E=f(P)

anybody can help me? plzzz