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Abstract
It is shown that the classical problem of motion of an arbitrary number of particles along a straight line with binary itneraction (shx)−2 placed under the action of the Morse potential can be solved by using the Lax representation. Exact solution of the equations of motion is reduced to calculation of the matrix exponentials. Existence conditions are determined for the points of equilibrium. The coordinates of particles at those points are defined by zeros of the generalized Laguerre polynomials, which allows us to find explicit expressions for the equilibrium-state energy and frequencies of small oscillations around equilibrium. Comparison is made with the results obtained earlier for the discrete spectrum of the corresponding quantum systems.
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