# How to solve system of three nonlinear PDE?

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Alex on 12 May 2014
Answered: Bill Greene on 12 May 2014
Hello, can you help with the solving following system of nonlinear PDE. All functions are complex. t,z are the only variables
i*dF/dt = c1(d^2F/dz^2)-c2(E*)G+c3*|F|^2*F
i*dG/dt = c1(d^2G/dz^2)-c2(E)F
i*dE/dt= -(d^2E/dz^2) - c4*E - c5(F*)E
i - imaginary one, c1-5 known constants, (E*) and (F*) are complex conjugate to the E and F,|F| is absolute value of F. Can I use 'pdenolin' in this case or not?

Bill Greene on 12 May 2014
pdenonlin is for solving only PDE that are not a function of time.
However, the parabolic function can solve equations that are first-order in time and have complex coefficients that are functions of the dependent variables (nonlinear).
Since you have only one spatial independent variable, z, the pdepe function in core MATLAB can also be used to solve this system.
Bill

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