Time-Dependent Polynomials with One Double Root, and Related New Solvable Systems of Nonlinear Evolution Equations

Calogero, F.: New solvable variants of the goldfish many-body problem. Stud. Appl. Math. 137(1), 123–139 (2016). https://doi.org/10.1111/sapm.12096

Bihun, O., Calogero, F.: A new solvable many-body problem of goldfish type. J. Nonlinear Math. Phys. 23, 28–46 (2016)

Bihun, O., Calogero, F.: Novel solvable many-body problems. J. Nonlinear Math. Phys. 23, 190–212 (2016)

Bihun, O., Calogero, F.: Generations of monic polynomials such that the coefficients of the polynomials of the next generation coincide with the zeros of polynomial of the current generation, and new solvable many-body problems. Lett. Math. Phys. 106(7), 1011–1031 (2016)

Calogero, F.: A solvable $$N$$ N -body problem of goldfish type featuring $$N^{2}$$ N 2 arbitrary coupling constants. J. Nonlinear Math. Phys. 23, 300–305 (2016)

Calogero, F.: Three new classes of solvable $$N$$ N -body problems of goldfish type with many arbitrary coupling constants. Symmetry 8, 53 (2016)

Bruschi, M., Calogero, F.: A convenient expression of the time-derivative $$z_{n}^{(k)}(t)$$ z n ( k ) ( t ) , of arbitrary order $$k$$ k , of the zero $$z_{n}(t)$$ z n ( t ) of a time-dependent polynomial $$p_{N}(z;t)$$ p N ( z ; t ) of arbitrary degree $$N$$ N in $$z$$ z , and solvable dynamical systems. J. Nonlinear Math. Phys. 23, 474–485 (2016)

Calogero, F.: Novel isochronous $$N$$ N -body problems featuring $$N$$ N arbitrary rational coupling constants. J. Math. Phys. 57, 072901 (2016). https://doi.org/10.1063/1.4954851

Calogero, F.: Yet another class of new solvable $$N$$ N -body problems of goldfish type. Qual. Theory Dyn. Syst. 16(3), 561–577 (2017). https://doi.org/10.1007/s12346-016-0215-y

Calogero, F.: New solvable dynamical systems. J. Nonlinear Math. Phys. 23, 486–493 (2016)

Calogero, F.: Integrable Hamiltonian $$N$$ N -body problems in the plane featuring $$N$$ N arbitrary functions. J. Nonlinear Math. Phys. 24(1), 1–6 (2017)

Calogero, F.: New C-integrable and S-integrable systems of nonlinear partial differential equation. J. Nonlinear Math. Phys. 24(1), 142–148 (2017)

Bihun, O., Calogero, F.: Generations of solvable discrete-time dynamical systems. J. Math. Phys. 58, 052701 (2017). https://doi.org/10.1063/1.4928959

Calogero, F.: Zeros of Polynomials and Solvable Nonlinear Evolution Equations. Cambridge University Press, Cambridge (2018). (in press)

Calogero, F.: Motion of poles and zeros of special solutions of nonlinear and linear partial differential equations, and related “solvable” many body problems. Nuovo Cimento 43B, 177–241 (1978)

Calogero, F.: Classical Many-Body Problems Amenable to Exact Treatments. Lecture Notes in Physics m66. Springer, Heidelberg (2001)

Calogero, F.: Isochronous Systems. Oxford University Press, Oxford (2008) (250 pages; marginally updated paperback version, 2012)

Gómez-Ullate, D., Sommacal, M.: Periods of the goldfish many-body problem. J. Nonlinear Math. Phys. 12(Suppl. 1), 351–362 (2005)

Calogero, F., Gómez-Ullate, D.: Asymptotically isochronous systems. J. Nonlinear Math. Phys. 15, 410–426 (2008)