1,721,283 research outputs found
Two new solvable dynamical systems of goldfish type
No full textTwo new solvable dynamical systems of goldfish type are identified, as well as their isochronous variants. The equilibrium configurations of these isochronous variants are simply related to the zeros of appropriate Laguerre and Jacobi polynomials. © 2010 The Author(s)
Isochronous oscillators
No full textWe exhibit the solution of the initial-value problem for the system of 2N + 2 oscillators characterized by the Hamiltonian where N is an arbitrary positive integer, Ω, b and ωn 2 are N + 2 arbitrary real constants, q̂m, q̂m with m = 0,1,⋯,N are the 2N + 2 canonical coordinates and p̂m, p̌m the corresponding 2N + 2 canonical momenta. In the classical context the solution is completely periodic with period T = 2π/|Ω| (for arbitrary initial data). In the quantal context the (infinitely degenerate) spectrum is equispaced, with spacing ħ|Ω|; all the corresponding eigenfunctions are also exhibited. This finding obtains as special case of a more general (new) class of isochronous Hamiltonians. © 2010 The Author(s)
Nonlinear evolution equations solvable by the inverse spectral transform
No full textedited by Dell'Antonio G., Doplicher S., Jona-Lasinio G
Spectral transform and solitons: an introduction to a novel technique to solve (certain classes of) nonlinear evolution equations
No full textedited by Cohen E. G. D
Spectral transform and solitons: tools to solve and investigate nonlinear evolution equations
No full text- …
