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The Schrödinger-Poisson system textstylebegin{cases} -triangle u+u+qK x phi u=f x,u), & xin mathbb {R}^{3}, -trianglephi=K x u^{2}, & xin mathbb {R}^{3}, end{cases} (1.3) describes a charged wave interacting with its own electrostatic field [2].
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A magnetic geodesic describes the trajectory of a charged particle in a Riemannian manifold M under the influence of an external magnetic field.
A significant example is that equation (1.1) describes the dynamics of a charged particle in electric and magnetic fields when the particle velocities are relativistic [1].
For example, the Schrödinger-Poisson system can describe the interaction of a charged particle with its own electrostatic field in quantum mechanics.
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