Research

"Computers are incredibly fast, accurate, and stupid; humans are incredibly slow, inaccurate, and brilliant; together, they are powerful beyond imagination." -- Einstein

• Geometric stabilization of S=2 vortices in lattices: theoretical analysis, numerical computation and experimental results. K.J.H. Law, D. Song, P.G. Kevrekidis, and Z. Chen. In preparation.
• Manipulation of Vortices by Localized Impurities in Bose-Einstein Condensates. M.C. Davis, R Carretero-Gonzalez, Z. Shi, K.J.H. Law, P.G. Kevrekidis,and B.P. Anderson. Submitted to Phys. Rev. A.
• A two-dimensional paradigm for symmetry breaking: the nonlinear Schroedinger equation with a four-well potential. C. Wang, G. Theocharis, P. G. Kevrekidis, N. Whitaker, K. J. H. Law, D. J. Frantzeskakis, and B.A. Malomed. Submitted to Phys. Rev. A.
• Interaction of excited states in two-species Bose-Einstein condensates: a case study. Todd Kapitula, K.J.H. Law and P.G. Kevrekidis. Submitted to SIADS.
• Numerical Methods in DNLS. K.J.H. Law, P.G. Kevrekidis. Chapter in the book "Discrete Nonlinear Schroedinger Equation: Mathematical Analysis, Numerical Computations, and Physical Perspectives". (ed. P.G. Kevrekidis)
• The Dynamics of Unstable Waves. Kody J.H. Law and Q. Enam Hoq. Chapter in "Discrete Nonlinear Schroedinger Equation : Mathematical Analysis, Numerical Computations, and Physical Perspectives". (ed. P.G. Kevrekidis)
• Vortex solutions of the discrete Gross-Pitaevskii equation. J. Cuevas, G. James, P.G. Kevrekidis, and K.J.H. Law. Phys. D - in Press, Corrected Proof, Available online 14 October 2008.
• Localized structures in Kagome lattices. K.J.H. Law, Avadh Saxena, P.G. Kevrekidis, and A.R. Bishop. Phys. Rev. A 79, 053818 (2009).
• Observation of double-charge discrete vortex solitons in hexagonal photonic lattices. Bernd Terhalle, Tobias Richter, Kody J. H. Law, Dennis Gories, Patrick Rose, Tristram J. Alexander, PanayotisG. Kevrekidis, Anton S. Desyatnikov,Wieslaw Krolikowski, Friedemann Kaiser, Cornelia Denz, and Yuri S. Kivshar. Phys. Rev. A 79, 043821 (2009).
• Stable higher-charge discrete vortices in hexagonal photonic lattices. Kody J.H. Law, Panayotis G. Kevrekidis, Tristram J. Alexander, Wieslaw Krolikowski, and Yuri S. Kivshar. Phys. Rev. A. 79, 025801 (2009).
• Discrete solitons and vortices in hexagonal and honeycomb lattices: existence, stability, and dynamics. K.J.H. Law, P.G. Kevrekidis, V. Koukouloyannis, I. Kourakis, D.J. Frantzeskakis, and A.R. Bishop. Phys. Rev. E 78, 066610 (2008).
• Dipole and quadrupole solitons in optically-induced two-dimensional defocusing photonic lattices. H. Susanto, K.J.H. Law, P.G. Kevrekidis, L. Tang, C. Lou, X. Wang, and Z. Chen. Phys. D 237, 3123-3134 (2008).
• Self-trapping of optical vortices in photonic lattices optically induced with self-defocusing nonlinearity. D.Song, L. Tang, C. Lou, X. Wang, J. Xu, Z. Chen, H. Susanto, K.J.H. Law and P.G. Kevrekidis. Opt. Exp., 16, 14, 10110 (2008).
• Averaging of Nonlinearity Management with Dissipation. Shabnam Beheshti, Kody J. H. Law, Panayotis G. Kevrekidis, and Mason A. Porter. Phys. Rev. A 78, 025805 (2008).
• Solitons and vortices in honeycomb defocusing photonic lattices. K.J.H. Law, H. Susanto, and P.G. Kevrekidis. Phys. Rev. A 78, 033802 (2008).
• Discrete breathers, multibreathers and vortices in 2D dust crystals. V. Koukouloyannis, P.G. Kevrekidis, I. Kourakis, D. Frantzeskakis, K.J.H. Law. 35th EPS Conference on Plasma Physics (2008).
• Emergence of Unstable Modes in an Expanding Domain for Energy-Conserving Wave Equations. K.J.H. Law, P.G. Kevrekidis, D.J. Frantzeskakis, and A.R. Bishop. Phys. Lett. A 372, 658 (2008).
• Stability of Quantized Vortices in a Bose-Einstein condensate confined in an Optical Lattice.K.J.H. Law, L. Qiao, P.G. Kevrekidis, and Y.G. Kevrekidis. Phys. Rev. A 77, 053612 (2008).
• Trapping of Two-component matter-wave solitons by mismatched optical lattices. Z. Shi, K.J.H. Law, P.G. Kevrekidis, and B.A. Malomed. Phys. Lett. A 372, 4021 (2008).
• Structure and stability of two-dimensional Bose-Einstein condensates under both harmonic and lattice confinement. K.J.H. Law and P.G. Kevrekidis, B.P. Anderson, R. Carretero-Gonzalez, and D.J. Frantzeskakis. J. Phys. B: At. Mol. Opt. Phys. 41 195303 (2008).
• Observation of dipole-like gap solitons in self-defocusing waveguide lattices. Liqin Tang, Cibo Lou, Xiaosheng Wang, Zhigang Chen, H. Susanto, K.J.H. Law and P.G. Kevrekidis. Opt. Lett., 32, 20, 3011 (2007).