Rodica D. Costin

Papers and preprints


Click here for recent preprints.

The Weber equation as a normal form with applications to the top of the barrier scattering, with Hyejin Park and Wilhelm Schlag

A direct method to find Stokes multipliers in closed form for P1 and more general integrable systems. with O. Costin and M. Huang.
Transactions of the AMS (to appear)

 Tronquée solutions of the Painlevé equation P1. with O. Costin, and M. Huang.
Constr. Approx. 41(2015), no. 3, 467-494

Explicit derivation of return maps for planar vector fields with nilpotent linear part with a center or a focus.
Anal. Appl.(Singap.) 11(2013),no.3, 17pp

Orthogonality of Jacobi and Laguerre polynomials for general parameters via the Hadamard finite part,
J. Approx. Theory 162 (2010), no. 1, 141--152.

Differential systems with Fuchsian linear part: correction and linearization, normal forms and multiple orthogonal polynomials.
J. Differential Equations 247 (2009), no. 7, 2074--2093.

The return map for a planar vector field with nilpotent linear part: a direct and explicit derivation.
Int. J. Math. Math. Sci. 2009, Art. ID 590856, 11 pp.

A class of matrix-valued polynomials generalizing Jacobi Polynomials,
J. Approx. Theory 161 (2009), no. 2, 787--801.

Matrix valued polynomials generated by the scalar-type Rodrigues' formulas,
J. Approx. Theory, 161 (2009), no. 2, 693--705

Nonlinear perturbations of Fuchsian systems: corrections and linearization, normal forms,
Nonlinearity 21, (2008), no.9, 2073-2082.

Analytic linearization of nonlinear perturbations of Fuchsian systems,
Nonlinearity 21, (2008), no.9, 2083-2095

Power and exponential-power series  solutions of evolution equations 
  Ann. Fac. Sci. Toulouse Math. (6)  13  (2004),  no. 4, 551--573   pdf

Time asymptotics of the Schrodinger wave function in time-periodic potentials
(with O. Costin, J Lebowitz, J.Stat.Phys., special issue
dedicated to Elliott Lieb on the occasion of his 70th birthday, 1-4, 283-310 (2004)

Rigorous estimates of Stokes constants for some nonlinear differential equations with rank one irregular singularity
(with M. Kohut, O. Costin; 
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 460 (2004), no. 2052, 3631--3641)

Nonintegrability criteria for a class of differential equations with two regular singular points
(with M. D. Kruskal; Nonlinearity, 16 (2003), no. 4, 1295--1317)   .pdf

Failure of analytic hypoellipticity in a class of PDOs
   (with O. Costin; Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 2 (2003), no. 1, 21--45.)

Asymptotic properties of a family of solutions of the Painleve equation PVI
(with O. Costin; Int. Math. Res. Not. 2002, no. 22, 1167--1182.)

Transition to the continuum of a particle in time-periodic potentials
   (with O. Costin, J L Lebowitz; Advances in Differential Equations and Mathematical Physics, AMS Contemporary Mathematics series ed. Karpeshina, Stolz, Weikard, and Zeng 2003)

Evolution of a model quantum system under time periodic forcing: conditions for complete ionization
    (With O. Costin,  A. Rokhlenko and J. Lebowitz; Comm. Math. Phys.  221, 1 pp 1--26 (2001))

Nonperturbative analysis of a model quantum system under time periodic forcing
   (With O. Costin, A. Rokhlenko and J. Lebowitz; Comptes Rendus Acad. Sci. Serie I, 332 5 pp 405--411 (2001))

On the formation of singularities of solutions of  nonlinear differential systems in antistokes directions
   (with O. Costin,  Inventiones Mathematicae 145, 3, pp 425-485 (2001) )

Singular normal form for the Painleve equation P1
   (with O. Costin,  Nonlinearity  Vol 11, No. 5 pp.  1195-1208 (1998))

Integrability Properties of Nonlinearly Perturbed Euler Equations
   (Nonlinearity Vol. 10 No 4 pp. 905-924 (1997))

Integrability Properties of a Generalized Lame Equation; Applications to the Henon-Heiles System
   (Meth.Appl.An., Vol 4 No 2, pp. 113-123 (1997) ) .pdf

Rigorous WKB for finite order linear recurrence relations with smooth coefficients
   (with O. Costin, SIAM.J.Math.Anal. v27 no1 (1996))

J. Stat.Phys.59 5/6 

J. Stat.Phys.64 1/2

On some linearization methods of the generalized flow rate characteristic of the hydraulic servomechanisms
Ursu, I., F. Popescu, M. Vladimirescu, Revue Roumaine des Sciences Techniques, Série de Mécanique Appliquée,
        Vol. 39, No. 2, pp. 207-21

Dynamic performances analysis for an electrohydraulic tracking system
(in Romanian, with
Ursu, I, M. Besliu, Studii si cercetari de mecanica aplicata, Vol. 51, No. 4, pp. 433-444, (1992))

  PhD Thesis (Rutgers University, 1997)  .pdf