PUBLICATIONS
Papers on Nonlinear
Schrödinger
Equation
- Kath, W.L. and Smyth, N.F., 1995,
Soliton evolution and radiation loss for the nonlinear Schrödinger
equation, Physical Review E, 51, pp.1484--1492
- Kath, W.L. and Smyth, N.F., 1998, Radiative losses due to pulse
interactions in birefringent nonlinear optical fibres, in Mathematical and Numerical Aspects of
Wave Propagation, J.A.
DeSanto, Ed., SIAM.
- Smyth, N.F. and Kath, W.L., 2001,
Radiative
losses due to pulse interactions in birefringent nonlinear optical
fibers, Physical Review E, 63, 036614
- Minzoni, A.A., Smyth, N.F. and Worthy,
A.L.,
2003,
Radiation from a Cut-off Point in a Two Layer Nonlinear TE Mode
Waveguide, Wave Motion, 37, pp. 25--42
- Minzoni, A.A., Smyth, N.F. and Worthy,
A.L.,
2005, A variational approach to the stability of an embedded NLS
soliton at the edge of the continuum, Physica
D, 206, pp. 166--179
Papers on Nonlinear Optics
- Malomed,
B.A., Parker, D.F. and Smyth,
N.F., 1993, Resonant shape oscillations and decay of a soliton in a
periodically inhomogeneous nonlinear optical fibre, Physical Review E, 48, pp.
1418--1425
- Malomed,
B.A. and Smyth, N.F., 1994,
Resonant splitting of a vector soliton in a periodically inhomogeneous
birefringent optical fibre, Physical
Review E, 50, pp.
1535--1542
- Malomed, B.A. and Smyth, N.F., 1994, Resonant splitting of
a vector soliton in a periodically inhomogeneous birefringent optical
fibre, Computational
Physics, P.L. Christiansen and E. Mosekilde (Editors), pp.
227--232.
- Smyth,
N.F. and Worthy, A.L., 1997,
Dispersive radiation and nonlinear twin-core fibres, Journal of the Optical Society of
America B, 14, pp.
2610--2617.
- Turitsyn,
S.K., Smyth, N.F. and Turitsyna,
E.G., 1998, Solitary waves in nonlinear dispersive systems with zero
average dispersion, Physical Review E,
58, pp. R44--R47
- Smyth,
N.F. and Pincombe, A.H., 1998,
Effect of radiative loss on pulses in periodically inhomogeneous
birefringent optical fibres, Physical
Review E, 57, pp.
7231--7238
- McKinnon,
K.I.M., Smyth, N.F. and Worthy,
A.L., 1999, Optimisation of soliton amplitude in dispersion decreasing
nonlinear optical fibres, Journal of
the Optical Society of America B,
16, pp. 441--447
- Smyth,
N.F., 2000, Soliton-effect
compression and dispersive radiation, Optics
Communications, 175,
pp. 469--475
- Beech-Brandt,
J.J. and Smyth, N.F., 2001,
Pulse evolution in nonlinear optical fibres with sliding-frequency
filters, Physical Review E, 63, 056604
- Ingledew,
G., Smyth, N.F. and Worthy, A.L.,
2003, Raman Induced Destabilisation of Asymmetric Coupled Solitary
Waves in Nonlinear Twin-Core Fibres, Optics
Communications, 218,
pp. 255--271
Papers
on Liquid Crystals
- García-Reimbert,
C., Garza-Hume, C., Minzoni, A.A., Reyes, J.A., Rodríguez, R.F.
and
Smyth, N.F., 2000, Active propagation and cut-off for low TM modes in a
nonlinear nematic waveguide, Physica
D, 145, pp. 144--157
- García-Reimbert,
C., Garza-Hume, C.E.,
Minzoni, A.A. and Smyth, N.F., 2002, Active TM mode envelope soliton
propagation in a nonlinear nematic waveguide, Physica D, 167, pp. 136--152
Papers
on Solitons in Liquid Crystals
(Nematicons)
- García
Reimbert, C., Minzoni, A.A. and
Smyth, N.F., 2006, Spatial soliton evolution in nematic liquid crystals
in the nonlinear local regime, Journal
of the Optical Society of
America B, 23, pp.
294--301.
- García-Reimbert,
C., Minzoni, A.A., Smyth, N.F. and Worthy, A.L., 2006, Large-amplitude
nematicon propagation in a liquid crystal with local response, Journal of the Optical Society of America B,
23, pp. 2551--2558.
- Minzoni, A.A., Smyth, N.F. and
Worthy, A.L., 2007, Modulation solutions for nematicon propagation in
non-local liquid crystals, Journal
of the Optical Society of America B, 24, pp. 1549--1556.
- Minzoni, A.A., Smyth, N.F., Worthy,
A.L., and Kivshar, Y.S., 2007, Stabilization of vortex solitons in
nonlocal nonlinear media, Physical
Review A, 76, 063803.
- Skuse, B.D., and Smyth,
N.F., 2008, Two-colour vector soliton interactions in nematic liquid
crystals in the local response regime, Physical Review A, 77, 013817.
- García-Reimbert, C.,
Minzoni, A.A., Skuse, B.D., Smyth, N.F., Marchant, T.R., and Worthy,
A.L.,
2008, Mathematical modelling of nematicons and their interactions, Proceedings of the Winter
Topical Meeting Series, 2008 IEEE/LEOS, pp. 119--120.
- García Reimbert, C., Minzoni,
A.A., Smyth, N.F., and Worthy, A.L., 2008, Dipole soliton
formation in nematic liquid crystals, N.F., 2008, Proceedings of the Winter
Topical Meeting Series, 2008 IEEE/LEOS, pp. 123--124.
- Skuse, B.D., and Smyth,
N.F., 2008, Two-colour nematicon interactions in local crystals, Proceedings of the Winter
Topical Meeting Series, 2008 IEEE/LEOS, pp. 125--126.
- García-Reimbert, C.,
Minzoni, A.A., Marchant, T.R., Smyth, N.F. and Worthy, A.L., 2008,
Dipole soliton formation in a nematic liquid crystal in the nonlocal
limit, Physica D, 237, pp. 1088--1102.
- Assanto, G., Smyth, N.F., and
Worthy, A.L., 2008, Two colour, nonlocal vector solitary waves with
angular momentum in nematic liquid crystals, Physical Review A, 78, 013832.
- Marchant, T.R., and Smyth, N.F.,
2008, Nonlocal validity of an asymptotic one-dimensional nematicon
solution, Journal of Physics A:
Mathematical and Theoretical,
41, 365201.
- Assanto, G., Marchant,
T.R., and Smyth, N.F., 2008, ``Collisionless shock resolution in
nematic liquid crystals,'' Physical
Review A, 78, 063808.
- Assanto, G., Minzoni, A.A.,
Peccianti, M., and Smyth, N.F., 2009, "Optical solitary waves escaping
a wide trapping potential in nematic liquid crystals: modulation
theory," Physical Review A, 79, 033837.
- Alberucci, A., Assanto,
G., Buccoliero, D., Desyatnikov, A., Marchant, T.R., and Smyth, N.F.,
2009, "Modulation analysis of boundary induced motion of nematicons," Physical Review A, 79, 043816.
- Xu, Z., Smyth, N.F., Minzoni,
A.A., and Kivshar, Y.S., 2009, "Vector vortex solitons in nematic
liquid crystals," Optics Letters,
34, pp. 1414--1416.
- Skuse, B.D.,
and Smyth, N.F., 2009, "Interaction of two colour solitary waves in a
liquid crystal in the nonlocal regime,'' Physical Review A, 79, 063806.
- Minzoni, A.A., Smyth,
N.F., Xu, Z., and Kivshar, Y.S., 2009, "Stabilization of vortex-soliton
beams in nematic liquid crystals,"
Physical Review A, 79,
063808.
- Assanto, G., Skuse,
B.D., and Smyth, N.F., 2009, "Optical path control of spatial optical
solitary waves in dye-doped nematic liquid crystals,"
Photonics Letters of Poland,
1 (4) , 154--156.
- Assanto, G., Minzoni, A.A.,
and Smyth, N.F., 2009, "Light self-localization in nematic liquid
crystals: modelling solitons in nonlocal reorientational media,'' Journal of Nonlinear Optical Physics and
Materials, 18, pp.
657--691.
- Minzoni, A.A., Smyth,
N.F., and Xu, Z., 2010, "Stability of an optical vortex in a circular
nematic cell,'' Physical Review A,
81, 033816.
- Assanto, G., Skuse, B.D.,
and Smyth, N.F., 2010, "Solitary wave propagation and steering
through light-induced refractive potentials," Physical Review A, 81, 063811.
- Assanto, G., Minzoni, A.A., Smyth,
N.F., and Worthy, A.L., 2010, "Refraction of nonlinear beams by
localised refractive index changes in nematic liquid crystals," Physical Review A, 82, 053843.
- Assanto, G., García-Reimbert,
C., Minzoni, A.A., Smyth, N.F., and Worthy, A.L., 2011, ``Lagrange
solution for three wavelength solitary wave clusters in nematic liquid
crystals,'' Physica
D, 240, 1213--1219.
- Assanto, G., Smyth,
N.F., and Xia, W., 2011, ``Modulation analysis of nonlinear beam
refraction at an interface in liquid crystals,'' Physical Review A, 84, 033818.
- Minzoni, A.A.,
Sciberras, L.W., Smyth, N.F., and Worthy, A.L., 2011, ``Propagation of
optical spatial solitary waves in bias-free nematic liquid crystal
cells,'' Physical Review A, 84, 043823.
- Assanto, G.,
Marchant, T.R., Minzoni, A.A., and Smyth, N.F., 2011, "Reorientational
versus Kerr dark and grey solitary waves using modulation theory," Physical Review E, 84, 066602.
- Minzoni,
A.A., Sciberras, L.W., Smyth, N.F., and Worthy, A.L., 2011,
"Nonlinear optical beams in bounded nematic liquid crystal cells,'' ANZIAM Journal, 53, C373--C386.
- Alberucci, A.,
Assanto, G., Minzoni, A.A., and Smyth, N.F., 2012, "Scattering of
reorientational optical solitary waves at dielectric perturbations," Physical Review A, 85, 013804.
- Smyth, N.F., and Xia, W., 2012,
"Refraction and instability of optical vortices at an interface in a
liquid crystal," Journal of Physics
B: Atomic, Molecular and Optical Physics, 45, 165403.
- Minzoni, A.A., and Smyth, N.F., 2012,
"Theoretical Approaches to Nonlinear Wave Evolution in Higher Dimensions,"
Nematicons: Spatial Optical Solitons in
Nematic Liquid Crystals, ed. G. Assanto, John Wiley and Sons.
- Minzoni, A.A., Sciberras, L.W., Smyth, N.F., and Worthy, A.L., 2012,
"Vortices in Nematic Liquid Crystals,"
Nematicons: Spatial Optical Solitons in
Nematic Liquid Crystals, ed. G. Assanto, John Wiley and Sons.
- García-Reimbert, C., Minzoni, A.A., and Smyth, N.F., 2012,
"Interaction of Nematicons and Nematicon Clusters,"
Nematicons: Spatial Optical Solitons in
Nematic Liquid Crystals, ed. G. Assanto, John Wiley and Sons.
-
Assanto, G., Smyth, N.F., and Xia, W., 2012, "Refraction of nonlinear light beams in
nematic liquid crystals," Journal of Nonlinear Optical Physics and Materials, 21, 1250033.
-
Minzoni, A.A., Sciberras, L.W., Smyth, N.F., and Worthy, A.L. 2013, "Optical vortex
solitary wave in a bounded nematic-liquid-crystal cell,"
Physical Review A,
87, 013810.
Papers on Nonlinear Optical Beams in
Colloids
- Marchant, T.R. and Smyth, N.F.,
2012, "Semi-analytical solutions for dispersive shock waves in colloidal
media," Journal of Physics B: Atomic,
Molecular and Optical Physics
45, 145401.
- Marchant,
T.R., and Smyth, N.F., 2012,
"Optical waves in soft media,'' Journal of Physics B: Atomic, Molecular and Optical Physics,
- Marchant, T.R. and Smyth, N.F.,
2012, "Solitary waves and their stability in colloidal media: semi-analytical solutions," Dynamics of Continuous, Discrete and Impulsive Systems-B,
19, 525--541.
Papers on Nonlinear Optical Beams in
Thermal Media
- Louis, S.A., Marchant, T.R., and Smyth, N.F.,
2013, "Optical solitary waves in thermal media with non-symmetric boundary conditions,"
Journal of Physics A: Mathematical and
General, 46, 055201.
- Louis, S.A.,
Marchant, T.R., and Smyth, N.F., 2013, "Temperature-induced deflection of optical solitons,"
Journal of Physics A: Mathematical and
General,
Papers
on Korteweg-de Vries
and Related Equations
- Kath,
W.L. and Smyth, N.F., 1995, Soliton
evolution and radiation loss for the Korteweg-de Vries equation, Physical Review E, 51, pp.
661--670
- Smyth,
N.F. and Worthy, A.L., 1995, Solitary wave
evolution for mKdV equations, Wave
Motion, 21, pp. 263--275
- Minzoni,
A.A. and Smyth, N.F., 1996, Evolution of
lump solutions for the KP equation, Wave
Motion, 24, pp. 291--305
- Marchant, T.R. and Smyth, N.F.,
1996, Solitary wave interaction
for the extended Korteweg-de Vries equation, IMA Journal of Applied Mathematics, 56(2), pp. 157--176.
- Cruz-Pacheco,
G., Flores-Reyna, G., Jorge,
M.C., Minzoni, A.A. and Smyth, N.F., 1998, Approximate evolution of
lump
initial conditions for the Benjamin-Ono equation, Wave Motion, 28, pp. 195--202
- Jorge,
M.C., Minzoni, A.A. and Smyth, N.F.,
1999, Modulation solutions for the Benjamin-Ono equation, Physica D, 132, pp. 1--18
- Marchant,
T.R. and Smyth, N.F., 2002, The initial-boundary
problem for the Korteweg-de Vries equation on the negative
quarter-plane, Proceedings of
the
Royal Society of London, Series A, 458, pp. 857--871.
- El, G.,
Grimshaw, R.H.J. and Smyth, N.F., 2006, Unsteady undular bores in fully
nonlinear shallow-water theory, Physics
of Fluids A, 18, 027104.
- Marchant,
T.R. and Smyth, N.F., 2006, An undular bore solution of the
Camassa-Holm equation, Physical
Review E, 73, 057602.
- Marchant,
T.R. and Smyth, N.F., 2006, An undular bore solution for the
higher-order Korteweg-de Vries equation, Journal of Physics A: Mathematical and General, 39, pp.
L563--L569.
- El, G.A., Grimshaw, R.H.J., and
Smyth, N.F., 2008, Asymptotic description of solitary wave trains in
fully
nonlinear shallow-water theory, Physica
D, 237, pp.
2423--2435.
Papers
on Resonant
(Transcritical) Flow over Topography
- Smyth,
N.F., 1987, Modulation theory
solution for resonant flow over topography, Proceedings of the Royal
Society of London A, 409,
pp. 79--97.
- Smyth, N.F., 1988,
Dissipative effects on the resonant flow of a
stratified fluid over topography, Journal
of Fluid Mechanics, 192, pp. 287--312.
- Marchant, T.R. and Smyth,
N.F., 1990, The extended Korteweg-de
Vries equation and the resonant flow of a fluid over topography, Journal of Fluid Mechanics, 221, pp. 263--288.
- El, G., Grimshaw, R.H.J., and Smyth,
N.F., 2009, Transcritical shallow-water flow past topography:
finite-amplitude theory,
Journal of Fluid Mechanics, 640, pp. 187--214.
Papers on Undular Bores
Papers on Discrete Systems
- Cisneros, L.A., Minzoni,
A.A., Panayotaros, P., and Smyth, N.F., 2008, ``Modulation analysis of
large scale discrete vortices,'' Physical
Review E, 78, 036604.
- Assanto, G.,
Cisneros, L.A., Minzoni, A.A., Skuse, B.D., Smyth, N.F., and Worthy,
A.L., 2010, "Soliton steering by longitudinal modulation of the
nonlinearity
in waveguide arrays," Physical
Review Letters, 104,
053903.
Papers
on Mathematical Biology
- Herrera, J., Maza, M.A., Minzoni,
A.A.,
Smyth, N.F and Worthy, A.L., 2004, Davydov Soliton Evolution in
Temperature Gradients Driven
by Hyperbolic Waves, Physica D,
191, pp. 156--177
- Cruz-Pacheco, G., Esteva, L., Minzoni,
A.A.,
Panayotaros, P., Smyth, N.F., 2010, Modelación matemática
de la epidemia, La UNAM Ante la
Emergencia Sanitaria. Experiencia de la Epidemia de Influenza A(H1N1),
José Narro Robles y Jaime Martuscelli coordinadores, Universidad
Nacional Autónoma de México, Mexico City, Mexico.
Papers
on Sine-Gordon Equation
- Minzoni, A.A. and Smyth, N.F., 1997, A modulation solution of the
signalling problem for the equation of self-induced transparency in the
Sine-Gordon limit, Methods and
Applications of Analysis, 4(1),
pp. 1--10.
- Smyth, N.F. and Worthy, A.L., 1999,
Soliton evolution and radiation loss for the Sine-Gordon equation, Physical Review E, 60, pp.
2330--2336
- Minzoni, A.A., Smyth, N.F. and Worthy,
A.L.,
2001, Pulse evolution for a two dimensional Sine-Gordon equation, Physica D, 159, pp. 101--123
- Minzoni, A.A., Smyth, N.F. and Worthy,
A.L.,
2004, Evolution of two dimensional standing and travelling breather
solutions for the Sine-Gordon equation, Physica D, 189, pp. 167-187
Papers
on Black Holes
- Corichi, A., Cruz-Pacheco, G.,
Minzoni,
A.A., Padilla, P., Rosenbaum, M., Ryan, M.P., Smyth, N.F. and
Vukasinac, T., 2002, Quantum collapse of a small dust shell, Physical Review D, 65, 064006
- Cruz-Pacheco, G., Minzoni, A.A., Padilla, P., Rosenbaum, M.,
Ryan, M.P., Smyth, N.F., and Vukaṥinac, T., 2003, On the
possibility of wormhole formation due to quantum effects in the
gravitational collapse of a small dust shell, Revista Mexicana de Física, 49, Suplemento
2, pp. 122--124.
Papers
on Particle Physics: Skyrmions
- Cruz-Pacheco, G., Padilla, P.,
Minzoni,
A.A., Corichi, A., Rosenbaum, M., Ryan, M.P., and Smyth, N.F., 2000,
The effect of low momentum quantum fluctuations on a coherent field
structure, Physical Review D,
61, 105011
Papers
on Geophysics
- Smyth, N.F. and Holloway, P.E.,
1988, Hydraulic jump and undular
bore formation on a shelf break,
Journal of Physical Oceanography, 18(7), pp.
947--962.
- Smyth, N.F., 1990, Formation of one dimensional waves for
resonant flow
in a channel, Pure and Applied
Geophysics, 133(4), pp.
619--633.
- Song, I., Elphick, S.C., Main, I.G.,
Ngwenya,
B.T., Odling, N.W. and Smyth, N.F., 2004, One-dimensional fluid
diffusion induced by constant-rate flow injection: Theoretical analysis
and application
to the determination of permeability and specific storage of a
cored rock sample, Journal of
Geophysical Research, 109, B05207
- Marchant, T.R. and Smyth, N.F., 2005,
Approximate solutions for magmon propagation from a reservoir, IMA
Journal of Applied
Mathematics, 70, pp.
796--813.
Papers on
Nanotechnology
- Jorge, M.C.,
Cruz-Pacheco, G., Mier-y-Teran-Romero, L. and Smyth, N.F., 2005,
Evolution of Two Dimensional Lump Nanosolitons
for the Zakharov-Kuznetsov and Electromigration Equations, Chaos, 15, 037104.
- Cristobal Latome, J., Minzoni, A.A.,
Smyth, N.F. and Vargas, C.A., 2006, Evolution of Benjamin-Ono solitons
in the presence of weak Zakharov-Kutznetsov lateral dispersion, Chaos, 16, 043103.
- Flores, G., Mercado, G., Pelesko,
J.A., and Smyth, N.F., 2007, Analysis of the dynamics and
touchdown in a model of electrostatic MEMS, SIAM Journal of Applied Mathematics, 67, pp. 434--446.
Papers on Statistical Mechanics
- Kaupužs, J., Rimshans, J., and Smyth, N.F., 2006, Numerical
analysis of Fokker-Planck equation in ferroelectrics with regard to
polarization fluctuations, Electromagnetic
Fields in Mechatronics, Electrical and Electronic Engineering, Proceedings of ISEF’05, Studies in Applied Electromagnetics and
Mechanics, 27, IOS
Press, pp. 58--63.
- Kaupužs, J., Rimshans,
J., and Smyth, N.F., 2008, Polarization Kinetics in Ferroelectrics with
Regard to Fluctuations, Science and Modelling
and Simulation in Material Engineering, 16, 065004.
Papers on Microwave Heating
- Hill, J.M. and Smyth, N.F., 1990, On the mathematical analysis of
hot-spots arising from microwave heating, Mathematical Engineering in Industry,
2(4), pp. 267--278.
- Smyth, N.F., 1990, Microwave heating of bodies with temperature
dependent properties, Wave Motion,
12, pp. 171--186.
- Pincombe, A.H. and Smyth, N.F.,
1991,
Microwave heating of materials with low conductivity, Proceedings of
the Royal Society of London A, 433,
pp. 479--498.
- Smyth, N.F., 1992, Effect of
conductivity on hotspots, Journal of
the Australian Mathematical
Society, Series B, 33(4),
pp. 403--413.
- Marchant, T.R. and Smyth, N.F., 1993,
Microwave heating of materials with non-ohmic conductance, SIAM Journal
of Applied Mathematics, 53(6),
pp. 1591--1612.
- Pincombe, A.H. and Smyth, N.F.,
1994, Microwave heating of
materials with power law temperature dependencies, IMA Journal of Applied Mathematics, 52(2), pp. 141--176.
- García Reimbert, C.,
Minzoni, A.A. and Smyth, N.F., 1996,
Effect of radiation losses on hotspot formation and propagation in
microwave heating, IMA Journal of
Applied Mathematics, 57(2),
pp. 165--179.
Papers on Industrial Modelling
- Galloway, S.J. and Smyth, N.F., 1997, A numerical method for
predicting crystal micro-structure, Applied
Mathematical Modelling,
21, pp.
569--578.
Papers on Shock Waves
Papers on Fluid Mechanics
- Smyth, N.F., 1988, Mean flow
induced by the viscous critical
layer in a stratified fluid, Journal
of the Australian Mathematical Society, Series B, 29, pp.
352--373.
- Smyth, N.F., 1990, Propagation of
flame fronts, Journal of the
Australian Mathematical
Society, Series B, 31,
pp. 385--396.
- Smyth, N.F., 1990, Formation of one dimensional waves for
resonant flow in a channel, in Oceanic
Hydraulics, Birkhauser Verlag, Basel.
- Tang, S.M., Qin, S.D. and Smyth, N.F., 1993, "Numerical study on
nonlinear long waves excited by moving disturbances in three
dimensional fluids,'' Proceedings of
the Second International Conference on Fluid Mechanics, Beijing,
China, pp. 724--729.
- Marchant, T.R. and Smyth, N.F., 1998, Pulse evolution for
Marangoni-Bénard convection, Mathematical
and Computer Modelling,
28(10),
pp. 45--58.
Papers on Nonlinear Diffusion
- Smyth, N.F. and Hill, J.M., 1988,
High-order nonlinear diffusion, I.M.A.
Journal of Applied
Mathematics, 40, pp.
73--86.
- Smyth, N.F., 1992, Waiting-time behaviour for a fourth-order
nonlinear diffusion equation, Proceedings
of the Centre for Mathematics and its Applications, The
Australian National University, 30,
pp. 212--217.
General Publications