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You can think of a solution describing rotating string with finite length, the existence of which is based on the nonlinear aspect of EOM, contrast to other linear equations. More generally the strings can move as arbitrarily as they like, relating to variant of initial conditions and boundary conditions. Similar for the infinite length string t'Hooft ...


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I understand that the field theory is nonlinear, but what does that have to do with stretching the string with strong excitations? Maybe you're overthinking this one. Find a washing line or a guitar string, and twang it. As you do, look carefully. The string started off straight, but as you were about to let go, it was stretched. The string is elastic, like ...


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There are several definitions of nonlinear and each can be somewhat dependent on context. In your question, I would imagine one could say the perturbation was nonlinear if there were higher order terms altering the "shape" of the metric. You could also argue that the perturbations were nonlinear if they made it so the metric could not be expanded in the ...


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As a first step you can use a simple method, which is for every small time step $\Delta t$ approximate the acceleration as constant and use $\Delta v=a\Delta t$ for each direction, and then $\Delta x = v\Delta t$. These equations apply separately for each dimension, so calculate the x and y velocities first and then the resulting changes in position


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An exponentially decaying tail is almost like having no tail for all practical reasons. For example consider the yukawa potential for interaction through exchange of a massive particle, it is $\propto e^{-\mu r}/r$ which is even a stronger tail than the asymptotic behavior of the hyperbolic secant. There we say that the interaction has the the effective ...


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Short explanation: Physical systems are usually dissipative systems. Dissipative systems can be modelled with a 1st order ODE system. If you do your perturbation analysis on this system at the Hopf bifurcation and take higher orders into account, you end up with the Stuart-Landau equation. Hence by derivation, it describes the dynamics of a system ...



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