Department of Mathematics

   Online papers

1. Analytic methods for obstruction to integrability in discrete dynamical systems
                  (with M. Kruskal, to appear in Communications on Pure and Applied Mathematics)  pdf
2. Topological construction of transseries and introduction to generalized Borel summability (to appear in AMS CONM series)   pdf
3. Complex Singularity Analysis for a nonlinear PDEs
                  (with S Tanveer, submitted)  pdf
4. Analyzability in the context of PDEs and applications 
                   (with Saleh Tanveer,to appear in  Annales de la Faculte des  Sciences de Toulouse)  pdf
5. Nonlinear evolution  PDEs in :  existence and uniqueness of solutions, asymptotic and Borel summability
                   (with Saleh Tanveer, submitted)  pdf
6. Time asymptotics of the Schrödinger wave function in time-periodic potentials   Dedicated to Elliott Lieb on the occasion of his 70th birthday 
                     (with R D Costin and J L Lebowitz, to appear in J. Stat. Phys.)  pdf
7. Failure of analytic hypoellipticity in a class of PDOs  
                     (with R. D. Costin, Annali della Scuola Normale Superiore di Pisa, Serie V. Vol II. Fasc. I (2003)) pdf
8. Transition to the continuum of a particle in time-periodic potentials, 
                    (with R. D. Costin and J L Lebowitz in Advances in Differential Equations and Mathematical Physics,
                    AMS Contemporary Mathematics series ed. Karpeshina, Stolz, Weikard, and Zeng 2003)  pdf
9. Borel summation of adiabatic invariants (with  L. Dupaigne and M. D. Kruskal, Nonlinearity  17  No 4 1509-1519 (2004) ) pdf
10. Rigorous bounds of Stokes constants for some nonlinear ODEs at rank one irregular singularities 
                  (with R. D. Costin and M Kohut,  accepted at  Proc. Roy. Soc. Lond.)  pdf
11. Decay versus survival of a localized state subjected to harmonic forcing: exact results
                      (with  J L Lebowitz and A Rokhlenko, J. Phys. A: Math. Gen. 35, pp 8943-8951 (2002)) pdf
12. Movable singularities of solutions of difference equations in relation to solvability and a study of a superstable fixed point 
                  (with M D Kruskal,  Theoretical and Mathematical Physics, 133 (2): 1455-1462 (2002))  .pdf
13. Asymptotic properties of a family of solutions of the Painleve equation PVI 
                      (with R D Costin,  IMRN No 22 pp 1167-1182 (2002)) .pdf
14. On the formation of singularities of solutions of  nonlinear differential systems in antistokes directions  
                      (with R. D. Costin,  Inventiones Mathematicae 145, 3, pp 425-485 (2001)) .pdf    (Copyright owned by Inventiones)
15. Evolution of a model quantum system under time periodic forcing: conditions for complete ionization 
                      (With R. D. Costin,  A. Rokhlenko and J. Lebowitz; Comm. Math. Phys.  221, 1 pp 1-26 (2001)) pdf
16. Existence and uniqueness of solutions of nonlinear evolution systems of n-th order
                    partial differential  equations in the complex plane (with S. Tanveer)  .pdf
17. Resonance Theory for Schrödinger Operators (with A. Soffer; Commun. Math. Phys. 224 (2001)) pdf
18. Nonperturbative analysis of a model quantum system under time periodic forcing 
                      (With R. D. Costin, A. Rokhlenko and J. Lebowitz; Comptes Rendus Acad. Sci. Serie I, 332 5 pp 405-411 (2001)) pdf
19. Existence and uniqueness for a class of nonlinear higher-order partial differential equations in the complex plane
                      (with Saleh Tanveer. Communications on Pure and Applied Mathematics, Vol. LIII, 0001- 0026 (2000)) pdf
20. Exact Results for the Ionization of a Model Quantum System
                      (with A. Rokhlenko and J. Lebowitz) J. Phys. A: Math. Gen.  33 pp. 1--9 (2000) pdf
21. On the complete ionization of a periodically perturbed  quantum system
                       (with A. Rokhlenko and J. Lebowitz) (CRM  Proceedings and Lecture Notes 27 pp 51--61 (2001)) pdf
22. On optimal truncation of divergent series solutions of nonlinear differential systems; Berry smoothing.
                       (with Martin D. Kruskal, Proc. R. Soc. Lond. A  455, 1931-1956 (1999)  .pdf
23. Correlation between pole location and asymptotic behavior for Painlevé I solutions 
                        (Comm.  Pure and Appl. Math. Vol. LII, 0461-0478 (1999)) .ps.gz .dvi.gz
24. Singular normal form for the Painleve equation P1
                         (with R. D. Costin,  Nonlinearity  Vol 11, No. 5 pp.  1195-1208 (1998))  .pdf
25. On Borel summation and Stokes phenomena of nonlinear differential systems
                        ( Duke Math. J. vol 93, No2 (1998)) .ps.gz dvi.gz
26. Optimal uniform estimates and rigorous asymptotics beyond all orders for a class of ODE's
                        (with Martin D. Kruskal, Proc. Roy. Soc. Lond. 452 (1996)) .ps.gz
27. Rigorous WKB for finite order linear recurrence relations with smooth coefficients
                        (with R.D. Costin, SIAM.J.Math.Anal. v27 no1 (1996)) .ps.gz (or abstract jpg )
28. Exponential asymptotics, transseries, and generalized Borel summation for analytic rank one systems of ODE's  
                        (IMRN 8, (1995)) .ps.gz
29. Gaussian fluctuations in random matrices
                       (with Joel Lebowitz, Phys.Rev.Lett v 75  no 1 (1995)) pdf
30. Limit probability distributions for an infinite order phas transition model
                       J. Stat.Phys.64 1/2 jpg (abstract)
31. Infinite order phase transition in a classical spin system
                       J. Stat.Phys.59 5/6 jpg (abstract)
32. The infinite coordinationl limit for classical spin systems on irregular lattices 
                       J. Phys. A:Math.Gen.19 jpg (abstract)

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           Department of Mathematics,
           Hill Center, 110 Frelinghuysen Rd
           Rutgers, The State University of New Jersey
           Piscataway, NJ 08854-8019, USA