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Physics and mathematics

of nonlinear processes and models

(University "La Sapienza" , Rome, Italy)

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MARIO BRUSCHI

LIST OF SCIENTIFIC PUBLICATIONS

 

[Some references are given to "Mathematical Reviews" (MR) and "Zentralblatt fur Mathematik und ihre Grenzgebiete / Mathematics Abstracts" (ZB)]
 
 

  1. "Nonlinear evolution equations solvable by the inverse spectral associated to the matrix Schroedinger equation of rank 4" (con D. Levi e O. Ragnisco)

Il Nuovo Cimento B43 (1978) pp.251-270 (MR 57 : 11446)
 
 

  1. "On the zeros of combinations of Hermite polynomials" (con S. Ahmed and F. Calogero)

Lettere al Nuovo Cimento 21 (1978) pp. 447-452 ( MR 58 ; 6392)
 
 

  1. "Evolution equations associated to the triangular matrix Schroedinger problem solvable by the inverse spectral transform" (con D. Levi e O. Ragnisco)

Il Nuovo Cimento B45 (1978) pp. 225- 237 (MR 80a : 34020)
 
 

  1. "On the zeros of combinations of Laguerre polynomials" (con S. Ahmed)

Lettere al Nuovo Cimento 22 (1978) pp. 173-177
 
 

  1. "On the zeros of combinations of Jacobi polynomials" (con S. Ahmed)

Lettere al Nuovo Cimento 22 (1978) pp. 178-182
 
 

  1. "Discrete version of the modified Korteweg de Vries equation with x-dependent coefficients" (con D. Levi e O. Ragnisco)

Il Nuovo Cimento A48 (1978) pp.213-226 ( MR 80a : 35104)
 

 

 

  1. "Properties of the zeros of the classical polynomials and of Bessel functions" (con S. Ahmed, F. Calogero, M.A. Olshanetsky e A. M. Perelomov)

Il Nuovo Cimento 49B (1979) pp. 173-198 ( MR 80g : 33018)
 
 

  1. " On the algebra of certain matrices related to the zeros of Hermite polynomials"

Lettere al Nuovo Cimento 24 (1979) pp. 509-512 (MR 80f : 33013)
 
 

  1. "Discrete version of the nonlinear Schroedinger equation with linearly x-dependent coefficients" (con D. Levi e O. Ragnisco)

Il Nuovo Cimento A53 (1979) pp. 21-30 ( MR 80k : 76021)
 
 

  1. "Eigenvectors of a matrix related to the zeros of Hermite polynomials" (con F. Calogero)

Lettere al Nuovo Cimento 24 (1979) pp. 601-604 (MR 80f:33014)
 
 

  1. "On the algebra of certain matrices related to the zeros of Laguerre polynomials"

Lettere al Nuovo Cimento 14 (1979) pp.417-423 (MR 80i:33019)
 
 

  1. "Toda lattice and generalized wronskian technique" (con D. Levi e O. Ragnisco)

Journal of Physics A: Math. Gen. 13 (1980) pp.2531-2533 (MR 8le:35007 - ZB 445:35011)
 
 

  1. "The non abelian Toda lattice (discrete analogue of the matrix Schroedinger problem)" (con S.Manakov, O.Ragnisco e D.Levi)

Journal of Math. Phys. 21 (1980) pp.2749-2753 (MR 82b:58041-ZB 451:35054)
 
 

  1. "Evolution equations associated to the discrete analogue of the matrix Schroedinger problem solvable by the Inverse Spectral Transform" (con O. Ragnisco e D. Levi)

Journal of Math. Phys. 21 (1981) pp.2463-2471 (MR 83b:81022-ZB 513:35026)
 
 

 

  1. "Extension of the Zakharov-Shabat generalized inverse method to solve differential - difference and difference-difference equations" (con D. Levi e O. Ragnisco)

Il Nuovo Cimento A58 (1980) pp.56-66 (MR 82b:58042)
 
 

  1. "Existence of a Lax Pair for any member of the class of nonlinear evolution equations associated to the matrix Schroedinger spectral problem" (con O. Ragnisco)

Lettere al Nuovo Cimento 29 (1980) pp.321-326 (MR 83c:35100c - ZB 466:35030)
 
 

  1. "Extension of the Lax method to solve a class of nonlinear evolution equations with x-dependent coefficients associated to the matrix Schroedinger spectral problem" (con O. Ragnisco)

Lettere al Nuovo Cimento 29 (1980) pp.327-330 (MR 83c:35100c - ZB 466:35031)
 
 

  1. "Backlund transformations and Lax technique" (con O. Ragnisco)

Lettere al Nuovo Cimento 29 (1980) pp.331-334 (MR 83c:35100a - ZB 466:35032)
 
 

  1. "Nonlinear differential-difference equations, Backlund transformations and Lax technique" (con O. Ragnisco)

Journal of Physics A: Math. Gen. 14 (1981) pp.1075-1081 (MR 82j:58060 - ZB 471:35075)
 
 

  1. "Finite-dimensional matrix representations of the operators of differentation through the algebra of raising and lowering operators: general properties" (con F. Calogero)

Il Nuovo Cimento 62B (1981), pp. 337-352 (MR 83c : 15006)
 
  

  1. "Nonlinear differential difference matrix equations with n-dependent coefficients" (con O. Ragnisco)

Lettere al Nuovo Cimento 31 (1981), pp. 492-496 (MR 84d:39003)
 
 

  1. "The quantum Toda lattice"

(con D. Levi, M.A. Olshanetsky, A.M. Perelomov and O. Ragnisco)

Physics Letters A88 (1982), pp. 7-12 (MR 83d:81103)
 
 

  1. "Nonlinear evolution equations associated to the 3rd order differential scalar operator" (con O. Ragnisco)

Preprint I.F.U. 254 (1981)
 
 

  1. "The chiral field hierarchy" (con D. Levi e O. Ragnisco)

Physics Letters A88 (1982), pp. 379-382 (MR 84a:35253)
 
 

  1. "The discrete chiral field hierarchy" (con D. Levi e O. Ragnisco)

Lettere al Nuovo Cimento 33 (1982), pp.284-288 (MR 83j:58067)
 
 

  1. "Nonlinear partial differential equations and Backlund transformations related to the 4 - dimensional selfdual Yang-Mills equation" (con D. Levi e O. Ragnisco)

Lettere al Nuovo Cimento 33 (1982), pp.263-266 (MR 84h:58067)
 
 

  1. "The hamiltonian structure of the non-abelian Toda hierarchy" (con O.Ragnisco)

Journal of Mathematical Physics 24 (1983) pp. 1414-1421 (MR 85h:58076)
 
 

  1. "Continuous and discrete matrix Burgers hierarchies" (con D. Levi e O. Ragnisco)

Il Nuovo Cimento B74 (1983), pp.33-51 (MR 85f:35182)
 
 

  1. "On the inversion of the commutation operator" (con O. Ragnisco)

Lettere al Nuovo Cimento 38 (1983), pp.41-44 (MR 85a:15005)
 
 

 

  1. "On the solution of a linear matrix equation" (con O.Ragnisco)

Lettere al Nuovo Cimento 40 (1984) pp. 37-40 (MR 85k:15011)
 
 

  1. "On the solution of a new class of nonlinear evolution equations" (con O. Ragnisco)

Physics Letters 102A (1984), pp. 37-40 (MR 85h:33184)
 
 

  1. "The hamiltonian structure of a novel class of solvable nonlinear evolution equations" (con O. Ragnisco)

Physics Letters 102A (1984), pp. 13-14 (MR 86c:58041)
 
 

  1. "Nonlinear evolution equations associated with the chiral field spectral problem" (con O. Ragnisco)

Nuovo Cimento 88B (1985), pp. 119-139 (MR 87g:35194)
 
 

  1. "The Hamiltonian structure of a complex version of the Burgers equation" (con O. Ragnisco)

Jourmal of Math. Phys. 26 (1985), pp. 943-945 (MR 86m:58049)
 
 

  1. "Soliton surface" (con A. Sym, D. Levi e O. Ragnisco)

Lettere al Nuovo Cimento 44 (1985), pp. 529-536 (MR 87i:58088)
 
 

  1. "The Lax representation for an integrable class of relativistic dynamical systems" (con F. Calogero)

Commun. Math. Phys. 109 (1987), pp. 481-492
 
 

  1. "Zeros of arbitrary polynomials as eigenvalues of simple matrices"

Inverse Problems 3 (1987), pp. L41-L43
 
 

  1. "On new solvable many body dynamical system with velocity dependent forces" (con O. Ragnisco)

Inverse problems 4 (1988), pp. L15-L20
 
 

  1. "Recursion operator and Backlund transformations for the Ruijsenaars-Toda lattice" (con O. Ragnisco)

Phys. Lett. 129A (1988), pp. 21-25
 
 

  1. "Lax representation and complete integrability of the periodic relativistic Toda Lattice" (con O. Ragnisco)

Physics Letters A134 (1989), pp. 365-370
 
 

  1. "The periodic relativistic Toda Lattice: direct and inverse problem" (con O. Ragnisco)

Inverse Problems 5 (1989), pp. 389-405
 
 

  1. "On a new integrable Hamiltonian system with nearest neighbour interaction" (con O. Ragnisco)

Inverse Problems 5 (1989), pp. 983-998
 
 

  1. "On a method for computing eigenvalues and eigenfunctions of linear differential operators" (con R.G. Campos e E. Pace)

Il Nuovo Cimento 105 B (1990), pp. 131-163
 
 

  1. "General analytic solution of certain functional equations of addition type" (con F. Calogero)

SIAM J. Math. Anal. 21 (1990)
 
 

  1. "Integrable symplectic maps" (con O. Ragnisco, P.M. Santini e Tu Gui-Zhang)

Physica D - 49 (1991), pp 273-294
 
 

  1. "Integrable cellular automata" (con O. Ragnisco and P.M. Santini )

Physics Letters A 169 (1992), pp 151-160
 
 

  1. "Cellular automata in 1+1, 2+1 and 3+1 dimensions, constants of motion and coherent structures" (con P.M. Santini ]

Physica D - 70 (1994), pp 185-209
 
 

  1. "A cellular automaton for the Ulam conjecture"

Preprint Dip. Fis. N. 929; submitted to Comm. Math. Phys.
 
 

  1. "Knot symbols: a tool to describe and simplify knot diagrams"

International Journal of Theor. Phys. 35 (1996) pp. 711-740
 
 

  1. "Peakons, R-Matrix and Toda Lattice" (con O. Ragnisco )

Physica A, V. 228, N. 104 (1996) [special issue in honour H.W.Capel, invited paper]
 
 

  1. "Determinantal Solution of the Logistic Map"

J. Phys. A 31 (1998) pp. 153-155
 
 

  1. "Solvable and/or integrable and/or linearizable N-body problems in ordinary (three dimensional) space" (con F. Calogero)

 J.of Nonlinear Mathematical Physics, V. 7, N. 3 (2000) pp.303-385

 

 

  1. "On the integrability of certain matrix evolution equations" (con F. Calogero)

Phys. Lett. A 273 (2000) pp. 167-172

 

  1.  "Integrable systems of quartic oscillators" (con F. Calogero)

Phys. Lett. A 273 (2000) pp. 173-182

 

  1.  "The ABCs of magnetic monopole dynamics” (con E. Abadoglu e F. Calogero)

Theor. and Math Phys. , V.128, N. 1 (2001) pp 835-845

 

  1. "A discrete Schroedinger spectral problem and its associated evolution equations” (con M.Boiti, F. Pempinelli and B. Prinari)

J. Phys. A 36 (2003) pp 139-149

 

 

  1. "Convenient parametrizations of matrices in terms of vectors” (con F. Calogero)

Phys. Lett. A 327 (2004) pp. 312-319

 

  1. "Integrable systems of quartic oscillators II” (con F. Calogero)

Phys. Lett. A 327 (2004) pp. 320-326

 

  1. "New solvable nonlinear matrix evolution equations”

 

      J.of Nonlinear Mathematical Physics, V. 12, Supplement 1 (2005) pp.97-105

 

  1. "Cellular Automata” (con F. Musso)

Encyclopedia of Mathematical Physics, eds. J.-P. Franšoise, G.L. Naber and Tsou S.T.  Oxford: Elsevier, 2006 (ISBN 978-0-1251-2666-3), volume 1 pages 255-267

 

61. “Two cellular Automata for the 3x+1 Map”

       arXiv:nlin/0502061  [nlin.CG] (2005)

 

62.  “New Cellular Automata associated with the Schr÷dinger Discrete Spectral    Problem”    

      J.of Nonlinear Mathematical Physics, vol. 13 nr. 2 (2006) pp 205-210

 

 

63. “Novel variants of the goldfish many-body model” (con F. Calogero)

 

 J. Math. Phys. V. 47 (2006) pp. 022703:1-25

 

64. “Goldfishing: a new solvable many-body problem.” (con F. Calogero)

 

 J. Math. Phys. V. 47 (2006)  pp. 102701:1-35

 

65. “Proof of certain Diophantine conjectures and identification of remarkable  classes of orthogonal polynomials” (con F. Calogero e R. Droghei)

    J. Phys. A: Math. Theor. 40 (2007) PP. 3815-3829.

 

66. “Tridiagonal matrices, orthogonal polynomials and Diophantine relations. I.”    (con F.     Calogero e R. Droghei)

        J. Phys. A: Math. Theor. 40 (2007) 9793-9817.
 

67. “Tridiagonal matrices, orthogonal polynomials and Diophantine relations. II.” (con F.     Calogero e R. Droghei)

        J. Phys. A: Math. Theor. 40 (2007) 14759-14772.
 

68.    "A generalization of the Collatz problem and conjecture”

 arXiv 08105159vl  math NT  (2008)

  

69.    "Additional recursion relations, factorizations and Diophantine properties

         associated with the polynomials of the Askey scheme."

        (con F.Calogero e R.Droghei)

     Advances Math. Phys., Article ID 268134 (43 pages) (2009). 
     doi:10.1155/2009/268134.
 

70.     “Integrability, analyticity, isochrony, equilibria, small oscillations, and Diophantine relations: results from the stationary Burgers hierarchy” (con F. Calogero e R. Droghei)

J. Phys. A: Math. Theor.42, 454202 (9 pages) (2009).
 

71.    “Integrability, analyticity, isochrony, equilibria, small oscillations, and Diophantine relations: results from the stationary KdV hierarchy” (con F. Calogero e R. Droghei)

      Math. Phys. 50, 122701 (2009); doi:10.1063/1.3267067.
 

72.    “Polynomials defined by three-term recursion relations and satisfying a second recursion relation: connection with discrete integrability, remarkable (often Diophantine) factorizations “ (con F. Calogero e R. Droghei)

 (to appear)