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x ∈ T, t ∈ [0, T], / / 1 - tanh(x
x ∈ T, t ∈ [0, T], / / 1 - tanh(x

... a) Check that s(t, x ) indeed solves the NLS. Hint: Write the derivatives ∂t s and ∂ xx s in terms of s. b) Show that subproblem (II) can be solved exactly w.r.t. time t. Now let g( x ) = s(0, x ). c) Write a M ATLAB function to solve the NLS on the torus T applying Lie splitting. d) Write a M ATLAB ...
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