Hamiltonian System

*To*: mathgroup at smc.vnet.net*Subject*: [mg88054] Hamiltonian System*From*: Grandpa <acloninger at wustl.edu>*Date*: Wed, 23 Apr 2008 04:07:37 -0400 (EDT)

So I'm trying to solve the following Hamiltonian system using Mathematica. I posted this earlier, but I wanted to make sure it's not skipped over. solution = NDSolve[{x'[t] == 2p[t], x[0] == 2, p'[t] == I*(2 + 1/2)(I*x[t])^(1 + 1/2), p[0] == 1-2*I}, {x, p}, {t,0,10}, MaxSteps -> Infinity][[1]]; I'm letting E=1, so at all points t, it should be that (p[t]/.solution)^2-(I*x[t]/.solution)^(2+1/2)=1. That is the case until the function crosses a branch cut on the complex x-plane that runs from 0 to i*(Infinity). Once the function crosses the branch cut, the system no longer preserves E and the value changes to something around 1.3. How can I go about fixing this problem? I've already tried working with the precision and accuracy goals, and that didn't work. I also tried the SymplecticPartitionedRungeKutta method, but that didn't work either. I'm not sure what else to consider. Any help would be appreciated. Thanks, Alex