## Publication List

### Works Submitted or in Preparation:

- [S11] "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.]
- [S10] "Avoided Hamiltonian-Hopf bifurcations." [With R. Kollár. In preparation.]
- [S9] "Semiclassical soliton ensembles for the three-wave resonant interaction equations: asymptotic behavior for small time." [With R. Buckingham and R. Jenkins. In preparation.]
- [S8] "Long-time behavior for Benjamin-Ono." [With E. Blackstone, L. Gassot, and P. Gérard. In preparation.]
- [S7] "Universality in the Benjamin-Ono small dispersion limit." [With E. Blackstone, L. Gassot, P. Gérard, and M. Mitchell. In preparation.]
- [S6] "Zero-dispersion limit for Benjamin-Ono." [With E. Blackstone, L. Gassot, and P. Gérard. In preparation.]
- [S5] "A double-scaling limit for general rogue waves of infinite order." [With D. Bilman. In preparation.]
- [S4] "Asymptotic behavior of general rogue waves of infinite order." [With D. Bilman. In preparation.]
- [S3] "Talanov self-focusing and its non-generic character." [With R. Buckingham and R. Jenkins. In preparation.]
- [S2] "On strong zero-dispersion asymptotics for Benjamin-Ono soliton ensembles" [With E. Blackstone and L. Gassot. 56 pages. Submitted to
*Contemporary Mathematics*.] - [S1] "On stratification, large-scale tides, and temporal changes in surface tidal elevations: Two-layer analytical model." [With A. N. Wetzel, B. K. Arbic, I. Cerovecki, M. C. Hendershott, R. H. Karsten, and J. F. Molinari. 48 pages.]

### 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:

- [T2] "Perturbation theory and asymptotics," in
*The Princeton Companion to Applied Mathematics*, N. Higham, M. Dennis, P. Glendinning, P. Martin, F. Santosa, and J. Tanner, eds., Princeton University Press, Princeton, NJ, 2015. [pages 208-218] - [T1]
*Applied Asymptotic Analysis*, Graduate Studies in Mathematics, Vol. 75, AMS Publications, Providence, 2006. [467 pages]

### Book Reviews:

- [R2] Review of
*Nonlinear Dispersive Waves: Asymptotic Analysis and Solitons*by M. J. Ablowitz,*SIAM Rev.*,**54**, pages 837-841, 2012. - [R1] Review of
*Asymptotics and Borel Summability*by O. Costin, in*J. Approx. Th.*,**162**, pages 881-883, 2010.

### Publications in Refereed Journals:

- [J72] "Painlevé-III monodromy maps under the \(D_6\to D_8\) confluence and applications to the large-parameter asymptotics of rational solutions,"
*SIGMA***20**, 019 (77 pages), 2024. DOI: 10.3842/SIGMA.2024.019. [With A. Barhoumi, O. Lisovyy, and A. Prokhorov.] - [J71] "Differential equations for approximate solutions of Painlevé equations: Application to the algebraic solutions of the Painlevé-III (\(D_7\)) equation,"
*SIGMA***20**, 008 (27 pages), 2024. DOI: 10.3842/SIGMA.2024.008. [With R. Buckingham.] - [J70] "On the algebraic solutions of the Painlevé-III (D
_{7}) equation,"*Physica D***441**, 133493 (22 pages), 2022. DOI: 10.1016/j.physd.2022.133493. [With R. Buckingham.] - [J69] "Large-degree asymptotics of rational Painlevé-IV solutions by the isomonodromy method,"
*Constr. Approx.***56**, pages 233-443, 2022. DOI: 10.1007/s00365-022-09586-1. [With R. Buckingham.] - [J68] "Broader universality of rogue waves of infinite order,"
*Physica D***435**, 133289 (12 pages), 2022. DOI: 10.1016/j.physd.2022.133289. [With D. Bilman.] - [J67] "Extreme superposition: High-order fundamental rogue waves in the far-field regime." [With D. Bilman. 79 pages. To appear in
*Memoirs AMS*.] - [J66] "On the Maxwell-Bloch system in the sharp-line limit without solitons,"
*Comm. Pure Appl. Math.*,**77**, pages 457-542, 2024. DOI: 10.1002/cpa.22136. [With S. Li.] - [J65] "Universality near the gradient catastrophe point in the semiclassical sine-Gordon equation,"
*Comm. Pure Appl. Math.***75**, pages 1517-1641, 2022. DOI: 10.1002/cpa.22018. [With B.-Y. Lu.] - [J64] "Extreme superposition: rogue waves of infinite order and the Painlevé-III hierarchy."
*Duke Math. J.***169**, number 4, pages 671-760, 2020. DOI: 10.1215/00127094-2019-0066. [With D. Bilman and L. Ling.] - [J63] "Dispersive asymptotics for linear and integrable equations by the \(\overline{\partial}\) steepest descent method," in
*Nonlinear Dispersive Partial Differential Equations and Inverse Scattering*(P. D. Miller, P. A. Perry, J.-C. Saut, and C. Sulem, eds.), Fields Institute Communications**83**, pages 253-291, 2019. DOI: 10.1007/978-1-4939-9806-7_5. [With M. Dieng and K. D. T.-R. McLaughlin.] - [J62] "Rational solutions of the Painlevé-III equation: large parameter asymptotics,"
*Constr. Approx.***51**, pages 123-224, 2020. DOI: 10.1007/s00365-019-09463-4. [With T. Bothner. Open Access.] - [J61] "On the increasing tritronquée solutions of the Painlevé-II equation,"
*SIGMA***14**, 125 (38 pages), 2018. - [J60] "A study of the direct spectral transform for the defocusing Davey-Stewartson-II equation in the semiclassical limit,"
*Comm. Pure Appl. Math.***72**, pages 1474-1547, 2019. DOI: 10.1002/cpa.21822. [With O. Assainova, C. Klein, and K. T.-R. McLaughlin.] - [J59] "A robust inverse scattering transform for the focusing nonlinear Schrödinger equation,"
*Comm. Pure Appl. Math.***72**, pages 1722-1805, 2019. DOI: 10.1002/cpa.21819. [With D. Bilman.] - [J58] "The diffusion equation with nonlocal data,"
*J. Math. Anal. Appl.***466**, pages 1119-1143, 2018. DOI: 10.1016/j.jmaa.2018.05.064. [With D. A. Smith.] - [J57] "Rational solutions of the Painlevé-III equation,"
*Stud. Appl. Math.***141**, pages 626-679, 2018. DOI: 10.1111/sapm.12220. [With T. Bothner and Y. Sheng.] - [J56] "Rational solutions of the Painlevé-II equation revisited,"
*SIGMA***13**, 065 (29 pages), 2017. [With Y. Sheng.] - [J55] "Semiclassical soliton ensembles for the three-wave resonant interaction equations,"
*Comm. Math. Phys.***354**, pages 1015-1100, 2017. DOI: 10.1007/s00220-017-2897-7. [With R. Buckingham and R. Jenkins.] - [J54] "Dispersive hydrodynamics: Preface,"
*Physica D***333**, pages 1-5, 2016. DOI: 10.1016/j.physd.2016.07.002. [With G. Biondini, G. A. El, and M. A. Hoefer.] - [J53]
"On the generation of dispersive shock waves,"
*Physica D***333**, pages 66-83, 2016. DOI: 10.1016/j.physd.2016.04.011. - [J52] "On the spectral and modulational stability of periodic wavetrains for nonlinear Klein-Gordon equations,"
*Bulletin of the Brazilian Mathematical Society***47**, pages 417-429, 2016. ISSN 1678-7714. [With C. K. R. T. Jones, R. Marangell, and R. Plaza.] - [J51]
"The scattering transform for the Benjamin-Ono equation in the small-dispersion limit,"
*Physica D***333**, pages 185-199, 2016. DOI: 10.1016/j.physd.2015.07.012. [With A. N. Wetzel.] - [J50]
"Direct scattering for the Benjamin-Ono equation with rational initial data,"
*Studies in Applied Mathematics***137**, pages 53-69, 2016. DOI: 10.1111/sapm.12101. [With A. N. Wetzel.] - [J49]
"Dynamical Hamiltonian-Hopf instabilities of periodic traveling waves in Klein-Gordon equations,"
*Physica D***308**, pages 87-93, 2015. DOI: 10.1016/j.physd.2015.06.006. [With R. Marangell.] - [J48] "Large-degree asymptotics of rational Painlevé-II functions. Critical behavior."
*Nonlinearity***28**, pages 1539-1596, 2015. [With R. Buckingham.] - [J47]
"Initial-boundary value problems for the defocusing nonlinear Schrödinger equation in the semiclassical limit,"
*Studies in Applied Mathematics***134**, pages 276-362, 2015. DOI: 10.1111/sapm.12075. [With Z. Qin. Selected for "Highlights of the Year 2015"] - [J46] "Spectral and modulational stability of periodic wavetrains for the nonlinear Klein-Gordon equation,"
*Journal of Differential Equations***257**, pages 4632-4703, 2014. [With C. K. R. T. Jones, R. Marangell, and R. Plaza.] - [J45] "Large-degree asymptotics of rational Painlevé-II functions. Noncritical behavior,"
*Nonlinearity***27**, pages 2489-2577, 2014. [With R. Buckingham.] - [J44] "Graphical Krein signature theory and Evans-Krein functions,"
*SIAM Review***56**, pages 73-123, 2014. [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,"
*Contemporary Mathematics***593**, pages 29-81, 2013. [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*with Riemann-Hilbert methods,"^{z}*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. Notices***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.