My research belongs to applied nonlinear mathematics and physical applied mathematics, with focuses on the following three areas. A central theme is the study of nonlinear differential equations via analytical and numerical means.

Nonlinear waves; Metamaterials; Nonlinear optics

I am interested in nonlinear waves in optical and mechanical metamaterials. My prior work focused on nonlinear edge waves in optical and mechanical topological insulators. I have also worked on dispersive shock waves in the KP and 2D BO equations, and self-similar solutions to the 2D hyperbolic NLS equation.

Publications:

• [DOI] D. D. J. M. Snee and Y.-P. Ma. Edge solitons in a nonlinear mechanical topological insulator. Extreme Mechanics Letters, 100487 (2019).
• [DOI] M. J. Ablowitz, Y.-P. Ma, and I. Rumanov. A universal asymptotic regime in the hyperbolic nonlinear Schrödinger equation. SIAM J. Appl. Math. 77(4), 1248-1268 (2017).
• [DOI] M. J. Ablowitz, A. Demirci, and Y.-P. Ma. Dispersive shock waves in the Kadomtsev-Petviashvili and Two Dimensional Benjamin-Ono equations. Physica D 333, 84-98 (2016).
• [DOI] C. Chong, P. G. Kevrekidis, M. J. Ablowitz, and Y.-P. Ma. Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices. Phys. Rev. E 93, 012909 (2016).
• [DOI] M. J. Ablowitz and Y.-P. Ma. Strong transmission and reflection of edge modes in bounded photonic graphene. Opt. Lett. 40, 4635-4638 (2015).
• [DOI] M. J. Ablowitz, C. W. Curtis, and Y.-P. Ma. Adiabatic dynamics of edge waves in photonic graphene. 2D Materials 2 (2), 024003 (2015).
• [DOI] M. J. Ablowitz, C. W. Curtis, and Y.-P. Ma. Linear and nonlinear traveling edge waves in optical honeycomb lattices. Phys. Rev. A 90, 023813 (2014).

Bright (left) and Peregrine (right) edge solitons in a mechanical topological insulator.

Dispersive shock waves in the KP (left) and 2D BO (right) equations.

Climate dynamics; Statistical physics; Fluid mechanics

I am interested in meltwater patterns under-represented in climate models. My prior work focused on using statistical physics to explain the geometric characteristics of Arctic melt ponds. I have also worked on some fluid problems including Rayleigh-Bénard convection and Homann stagnation-point flow.

Publications:

• [DOI] Y.-P. Ma, I. Sudakov, C. Strong, and K. M. Golden. Ising model for melt ponds on Arctic sea ice. New Journal of Physics, 21(6), 063029 (2019).
• [DOI] P. Weidman and Y.-P. Ma. The competing effects of wall transpiration and stretching on Homann stagnation-point flow. Eur. J. Mech. B-Fluid 60, 237-241 (2016).
• [DOI] Y.-P. Ma and E. A. Spiegel. A diagrammatic derivation of (convective) pattern equations. Physica D 240, 150-165 (2011).

Metastable state in the random field Ising model (left) and aerial image of Arctic melt ponds (right).

Diagrams to derive the Swift-Hohenberg equation for Rayleigh-Bénard convection.

Pattern formation; Dynamical systems

I am interested in spatially localized states in driven dissipative systems. These solutions are often found using dynamical systems methods. My prior work focused on 1D and 2D localized Turing patterns in forced oscillatory systems. I have also worked on Turing-Hopf localized states in the 1D Brusselator model.

Publications:

• [DOI] Y.-P. Ma and E. Knobloch. Two-dimensional localized structures in harmonically forced oscillatory systems. Physica D 337, 1-17 (2016).
• [DOI] J. C. Tzou, Y.-P. Ma, A. Bayliss, B. J. Matkowsky, and V. A. Volpert. Homoclinic snaking near a codimension-two Turing-Hopf bifurcation point in the Brusselator model. Phys. Rev. E 87, 022908 (2013).
• [DOI] A. R. Champneys, E. Knobloch, Y.-P. Ma and T. Wagenknecht. Homoclinic snakes bounded by a saddle-center periodic orbit. SIAM J. Appl. Dyn. Syst. 11(4), 1583-1613 (2012).
• [DOI] Y.-P. Ma and E. Knobloch. Depinning, front motion and phase slips. Chaos 22, 033101 (2012).
• [DOI] Y.-P. Ma, J. Burke and E. Knobloch. Defect-mediated snaking: A new growth mechanism for localized structures. Physica D 239, 1867-1883 (2010).

2D localized hexagonal pattern in the 1:1 forced complex Ginzburg-Landau equation (FCGLE).

Defect-mediated snaking of 1D localized Turing patterns in the 1:1 FCGLE.