ode45 Runge Kutta

dx1/dz=0.5*beta2*x1*x4 evolution of amplitude

dx2/dz=-beta2*x5 evolution of position

dx3/dz=-beta2*x3*x4 evolution of width

dx4/dz=-4*beta2/x3^4+beta2*x4^2-gamma*x1^2/x3^2

dx5/dz=0

beta2 is dispersion of velocity group

gamma is nonlinear coefficient

[Torsten]

Use "ode45" instead of a self-written code to solve your system of differential equations.

And what are your equations for x4 and x5 ?

[Cris LaPierre]

Consider taking a look at some of the other questions asked about implementing a 4th order Runge-Kutta in MATLAB.

https://www.mathworks.com/matlabcentral/answers/?search_origin=ans_browse&term=Runge+Kutta+4

[Walter Roberson]

You still appear to be missing the equation for dx5/dz ?