The research on computing Lyapunov exponent for PDE's is restricted to single-variable equation. I want to calculate it for at least a two-variable equation. (for example u and v as dependent variable, t and x as independent, derivatives of u and v to t and x and available and u and v are two relevant variable). Is there any method for this purpose?
You may use Fourier transformation to convert linear PDE to ODE with
one independent variable and then construct the Lyapunov exponent for ODE. For example wave equation u_{tt}-u_{xx}=0 could be transformed by Fourier transformation to ODE v_{tt}+s^2v)(t,s)=0
Dear olfa
thanks for your answer.
In the shibata or zhao's paper, the considered equation is composed of one dependent variable (for example u) and it's derivatives to t and x (as independent variable). I want to calculate it for at least a two-variable equation. (for example u and v as dependent variable, t and x as independent, derivatives of u and v to t and x and available and u and v are two relevant variable). do you have any idea for this?
You may use Fourier transformation to convert linear PDE to ODE with
one independent variable and then construct the Lyapunov exponent for ODE. For example wave equation u_{tt}-u_{xx}=0 could be transformed by Fourier transformation to ODE v_{tt}+s^2v)(t,s)=0
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