New solvable many-body problems in the plane
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چکیده
منابع مشابه
New solvable many-body problems in the plane
We revisit an integrable (indeed, superintegrable and solvable) many-body model introduced almost two decades ago by Gibbons and Hermsen and by Wojciechowski, and we modify it so that its generic solutions are all isochronous (namely, completely periodic with fixed period). We then show how this model (or rather the more basic dynamical system that underlies its solvable character, and other av...
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A new class of solvable N -body problems is identified. They describe N unitmass point particles whose time-evolution, generally taking place in the complex plane, is characterized by Newtonian equations of motion “of goldfish type” (acceleration equal force, with specific velocity-dependent one-body and two-body forces) featuring several arbitrary coupling constants. The corresponding initial-...
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A solvable many-body problem in the plane is exhibited. It is characterized by rotation-invariant Newtonian (“acceleration equal force”) equations of motion, featuring one-body (“external”) and pair (“interparticle”) forces. The former depend quadratically on the velocity, and nonlinearly on the coordinate, of the moving particle. The latter depend linearly on the coordinate of the moving parti...
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First known examples of quasi-exactly-solvable N -body problems on the line are presented. These are related to the hidden algebra slN , and they are of two types – containing up to N and up to 6 body interactions only. Both types degenerate to the Calogero model. E-mail: [email protected] E-mail: [email protected] On leave of absence from the Institute for Theoretical and E...
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Abstract: Three new classes of N-body problems of goldfish type are identified, with N an arbitrary positive integer (N ě 2). These models are characterized by nonlinear Newtonian (“accelerations equal forces”) equations of motion describing N equal point-particles moving in the complex z-plane. These highly nonlinear equations feature many arbitrary coupling constants, yet they can be solved b...
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ژورنال
عنوان ژورنال: Journal of Nonlinear Mathematical Physics
سال: 2006
ISSN: 1776-0852
DOI: 10.2991/jnmp.2006.13.2.7