The N-Vortex Problem: Analytical Techniques

By P. Newton. 2001

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The blow up analysis of solutions of the elliptic sinh-Gordon equation (2007, background): “See for instance [9,18,21,23–25,28,42], and the references therein.”
Statistical Mechanics of Two-Dimensional Vortices and Stellar Systems (2002, methodology): “(99) Furthermore, the equations of motion (Newton’s equations) can be put in the Hamiltonian form m dri dt = ∂H ∂vi , m dvi dt = −∂H ∂ri , H = 1 2 N ∑ i=1 mv2i − ∑ i j Gm2 |ri − rj | .”
Temperature in and out of equilibrium: A review of concepts, tools and attempts (2017, background): “So the N point-vortices constitute a N degrees of freedom Hamiltonian system [94] with canonical coordinates qi = √ |Γi|xi, pi = √ |Γi|sign(Γi)yi.”