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Numerical Simulation of Damped, Driven Nonlinear Waves with Extended Initial Conditions

I am working on a project that requires creating a specific type of graph, but I am having trouble writing the correct code. The graph should look similar to the one I have attached below. There is also an open question on StackExchange Numerical Simulation of a Damped, Driven Nonlinear Wave System with Spatially Extended Initial Conditions . Could someone please provide guidance on how to correctly create this type of graph? Any help with the code or tips would be greatly appreciated!

Thank you in advance for your assistance!

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