Peter D. Miller

Professor of Mathematics

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Publication List

Works Submitted or in Preparation:

• [S5] "Rigorous asymptotics for the point spectrum of the nonselfadjoint Zakharov-Shabat eigenvalue problem with Klaus-Shaw potential" [With J. Bronski and K. T.-R. McLaughlin. In preparation.]
• [S4] "Initial-boundary value problems for the defocusing nonlinear Schrödinger equation in the semiclassical limit" [With Z. Qin. In preparation.]
• [S3] "The semiclassical modified nonlinear Schrödinger equation III: asymptotic analysis of the Cauchy problem. The hyperbolic region for transsonic initial data." [With J. DiFranco. In preparation.]
• [S2] "Large-m asymptotics of the rational solution to the mth inhomogeneous Painlevé II equation and related functions" [With R. Buckingham. In preparation.]
• [S1] "Modulational and spectral (in)stability of periodic wavetrains for the nonlinear Klein-Gordon equation" [With C. K. R. T. Jones, R. Marangell, and R. Plaza. In preparation.]

Research Monographs:

• [M2] Discrete Orthogonal Polynomials: Asymptotics and Applications, Annals of Mathematics Studies series, volume 164, Princeton University Press, Princeton, 2007. [With J. Baik, T. Kriecherbauer, and K. T.-R. McLaughlin. 184 pages.]
• [M1] Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation, Annals of Mathematics Studies series, volume 154, Princeton University Press, Princeton, 2003. [With S. Kamvissis and K. T.-R. McLaughlin. 265 pages.]

Textbooks:

• [T1] Applied Asymptotic Analysis, Graduate Studies in Mathematics, Vol. 75, AMS Publications, Providence, 2006. [467 pages]

Publications in Refereed Journals:

• [J44] "Graphical Krein signature theory and Evans-Krein functions", to appear in SIAM Review. [With R. Kollár. ]
• [J43] "On the stability analysis of periodic sine-Gordon traveling waves", Physica D, 251, pages 63-74, 2013. [With C. K. R. T. Jones, R. Marangell, and R. Plaza.]
• [J42] "The semiclassical modified nonlinear Schrödinger equation II: asymptotic analysis of the Cauchy problem. The elliptic region for transsonic initial data", to appear in Contemporary Mathematics. [With J. DiFranco.]
• [J41] "The sine-Gordon equation in the semiclassical limit: dynamics of fluxon condensates", Memoirs of the AMS, 225, number 1059, pages (i)-(v) and 1-136, 2013. [With R. Buckingham.]
• [J40] "The sine-Gordon equation in the semiclassical limit: critical behavior near a separatrix", Journal d'Analyse Mathématique, 118, pages 397-492, 2012. [With R. Buckingham.]
• [J39] "The Benjamin-Ono hierarchy with asymptotically reflectionless initial data in the zero-dispersion limit", Comm. Math. Sci., 10, pages 117-130, 2012. [With Z. Xu.]
• [J38] "On the modified nonlinear Schrödinger equation in the semiclassical limit: supersonic, subsonic, and transsonic behavior", Acta Math. Sci., 31, pages 2343-2377, 2011. [With J. DiFranco and B. Muite.]
• [J37] "On the zero-dispersion limit of the Benjamin-Ono Cauchy problem for positive initial data", Comm. Pure Appl. Math., 64, pages 205-270, 2011. [With Z. Xu.]
• [J36] "The ∂ steepest descent method for orthogonal polynomials on the real line with varying weights", Intern. Math. Res. Notices, 2008, Article ID rnn075, pages 1-66, 2008. [With K. T.-R. McLaughlin.]
• [J35] "Exact solutions of semiclassical non-characteristic Cauchy problems for the sine-Gordon equation", Physica D, 237, pages 2296-2341, 2008. [With R. Buckingham.]
• [J34] "The semiclassical modified nonlinear Schrödinger equation I: modulation theory and spectral analysis", Physica D, 237, pages 947-997, 2008. [With J. DiFranco.]
• [J33] "Locating the zeros of partial sums of e^z with Riemann-Hilbert methods", Contemporary Mathematics, 458, pages 183-195, 2008. [With T. Kriecherbauer, A. B. J. Kuijlaars, and K. T.-R. McLaughlin.]
• [J32] "Riemann-Hilbert problems with lots of discrete spectrum", Contemporary Mathematics, 458, pages 163-181, 2008.
• [J31] "The N-soliton of the focusing nonlinear Schrödinger equation for N large", Comm. Pure Appl. Math., 60, pages 951-1026, 2007. [With G. D. Lyng.]
• [J30] "The ∂ steepest descent method and the asymptotic behavior of polynomials orthogonal on the unit circle with fixed and exponentially varying nonanalytic weights", Intern. Math. Res. Papers, 2006, Article ID 48673, pages 1-78, 2006. [With K. T.-R. McLaughlin.]
• [J29] "Uniform asymptotics for polynomials orthogonal with respect to a general class of discrete weights and universality results for associated ensembles: announcement of results", Intern. Math. Res. Not., 2003, No. 15, pages 821-858, 2003. [With J. Baik, T. Kriecherbauer, and K. D. T.-R. McLaughlin.]
• [J28] "Asymptotics of semiclassical soliton ensembles: rigorous justification of the WKB approximation", Intern. Math. Res. Not., 2002, No. 8, pages 383-454, 2002.
• [J27] "On the semiclassical limit for the focusing nonlinear Schrödinger equation: sensitivity to analytic properties of the initial data", R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 458, pages 135-156, 2002. [With S. R. Clarke.]
• [J26] "Optimal tail estimates for directed last passage site percolation with geometric random variables", Advances Theor. Math. Phys., 5, pages 1207-1250, 2001. [With J. Baik, P. Deift, K. T.-R. McLaughlin, and X. Zhou.]
• [J25] "An exactly solvable model for the interaction of linear waves with Korteweg-de Vries solitons", SIAM J. Math. Anal., 33, pages 261-285, 2001. [With S. R. Clarke.]
• [J24] "Some remarks on a WKB method for the nonselfadjoint Zakharov-Shabat eigenvalue problem with analytic potentials and fast phase", Physica D, 152/153, pages 145-162, 2001.
• [J23] "Linear guidance properties of solitonic Y-junction waveguides", Opt. Quantum Electron., 33, pages 19-54, 2001. [With J. A. Besley and N. N. Akhmediev.]
• [J22] "On the generation of solitons and breathers in the modified Korteweg-de Vries equation", CHAOS, 10, pages 383-392, 2000. [With S. R. Clarke, R. Grimshaw, E. Pelinovsky, and T. Talipova.]
• [J21] "Soliton interactions in perturbed nonlinear Schrödinger equations", Phys. Rev. E, 61, pages 7121-7133, 2000. [With J. A. Besley and N. N. Akhmediev.]
• [J20] "Metastability of breather modes of time-dependent potentials", Nonlinearity, 13, pages 507-568, 2000. [With A. Soffer and M. I. Weinstein.]
• [J19] "A coupled Korteweg-de Vries system and mass exchanges among solitons", Physica Scripta, 61, pages 518-525, 2000. [With P. L. Christiansen.]
• [J18] "On the semiclassical limit of the focusing nonlinear Schrödinger equation", Phys. Lett. A, 247, pages 75-86, 1998. [With S. Kamvissis.]
• [J17] "Macroscopic dynamics in quadratic nonlinear lattices", Phys. Rev. E, 57, pages 6038-6049, 1998. [With O. Bang.]
• [J16] "Self-similar evolution of self-written waveguides", Opt. Lett., 29, pages 268-270, 1998. [With T. M. Monro, L. Poladian, and C. M. de Sterke.]
• [J15] "Modal expansions and completeness relations for some time-dependent Schrödinger equations", Physica D, 123, pages 513-524, 1998. [With N. N. Akhmediev.]
• [J14] "Periodic optical waveguides: exact floquet theory and spectral properties", Stud. Appl. Math., 101, pages 343-355, 1998. [With J. A. Besley and N. N. Akhmediev.]
• [J13] "Modes of periodic waveguides", Opt. Lett., 22, pages 1162-1164, 1997. [With J. A. Besley and N. N. Akhmediev.]
• [J12] "Effects of surface roughness on gratings", J. Opt. Soc. Am. B, 14, pages 1339-1344, 1997. [With F. Ladouceur and L. Poladian.]
• [J11] "Vector nonlinear Schrödinger hierarchies as approximate Kadomtsev-Petviashvili hierarchies", Physica D, 101, pages 17-26, 1997.
• [J10] "Optical conveyor belts: a new scheme for fiber communications", Opt. Lett., 21, pages 1132-1134, 1996. [With N. N. Akhmediev and A. Ankiewicz.]
• [J9] "Exploiting discreteness for switching in waveguide arrays", Opt. Lett., 21, pages 1105-1107, 1996. [With O. Bang.]
• [J8] "Modulation of multiphase waves in the presence of resonance", Physica D, 92, pages 1-27, 1996. [With N. M. Ercolani and C. D. Levermore.]
• [J7] "Zero-crosstalk junctions made from dark solitons", Phys. Rev. E, 53, pages 4137-4142, 1996.
• [J6] "Transfer matrices for multiport devices made from solitons", Phys. Rev. E, 53, pages 4098-4106, 1996. [With N. N. Akhmediev.]
• [J5] "Do solitons exchange conserved quantities during collisions?", Phys. Rev. Lett., 76, pages 38-41, 1996. [With N. N. Akhmediev.]
• [J4] "Finite genus solutions to the Ablowitz-Ladik equations", Comm. Pure Appl. Math., 48, pages 1369-1440, 1995. [With N. M. Ercolani, I. M. Krichever, and C. D. Levermore.]
• [J3] "Macroscopic lattice dynamics", Physica D, 79, pages 1-15, 1994. [With M. H. Hays and C. D. Levermore.]
• [J2] "The quantum discrete self-trapping equation in the Hartree approximation", Physica D, 69, pages 18-32, 1993. [With E. Wright, J. C. Eilbeck, M. H. Hays, and A. C. Scott.]
• [J1] "Binding energies for discrete nonlinear Schrödinger equations", Physica Scripta, 44, pages 509-516, 1991. [With A. C. Scott, J. Carr, and J. C. Eilbeck.]

Conference Proceedings:

• [C7] "Linear Y-junctions for modal splitting from periodic waveguides", 3rd Asia-Pacific Conference on Communications, Sydney, Australia, 1997. [With J. A. Besley and N. N. Akhmediev.]
• [C6] "X-junctions without cross-talk", Proceedings of the 21st Australian Conference on Optical Fibre Technology (ACOFT '96), Gold Coast, Queensland, Australia, 1996. [With N. N. Akhmediev.]
• [C5] "Power transfer in waveguide devices made from solitons", Nonlinear Guided Waves and their Applications, Cambridge, England. OSA Technical Digest Series, Volume 15, 1996. [With N. N. Akhmediev.]
• [C4] "Optical conveyor belts: a new scheme for fiber communications", Proceedings of the 20th Australian Conference on Optical Fibre Technology (ACOFT '95), Coolum Beach, Queensland, Australia, 1995. [With N. N. Akhmediev and A. Ankiewicz.]
• [C3] "Multi-port switching in waveguide arrays", Proceedings of the 20th Australian Conference on Optical Fibre Technology (ACOFT '95), Coolum Beach, Queensland, Australia, 1995. [With O. Bang.]
• [C2] "Exploiting discreteness for switching in arrays of nonlinear waveguides", Copenhagen Conference on Complex Dynamics in Spatially Extended Systems, Niels Bohr Institute, Copenhagen, Denmark, 1995. Physica Scripta, T67, pages 26-29, 1996. [With O. Bang.]
• [C1] "Macroscopic behavior in the Ablowitz-Ladik equations", in Nonlinear Evolution Equations and Dynamical Systems NEEDS 94, Makhankov, et. al, eds, World Scientific, 1995.

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