About

Mark J. Ablowitz is a CU Distinguished Professor in the Department of Applied Mathematics at the University of Colorado Boulder. His research interests include nonlinear phenomena, physical applied mathematics, and related fields. He is associated with the Applied Mathematics program located in the Engineering Center at CU Boulder, and his contact information includes an email address (mark.ablowitz@colorado.edu) and phone number (303-492-5502). His work focuses on the study and analysis of nonlinear phenomena within applied mathematics, contributing to the understanding of complex physical systems through mathematical modeling and analysis.

Research topics

• Quantum mechanics
• Physics
• Mathematics
• Geometry
• Mathematical physics
• Mathematical analysis

Selected publications

• Topological routing in Chern insulators

  arXiv (Cornell University) · 2026-04-15

  preprintOpen access1st authorCorresponding

  Chern insulator systems are realizable in numerous physical systems and can support robust nonreciprocal transmission of energy. A routing functionality constructed from two counter-oriented Chern insulator regions, using coupled Haldane type systems is proposed. By adjusting the strength of a magnetic field and the frequency of an antenna source, it possible to steer the flow of energy: completely to the left, completely to the right, or split. Alternatively, two sources can be used to direct the flow of energy. This formulation has the potential to serve as a robust and reconfigurable component in optical transmission.

  PublisherDOI

• Topological routing in Chern insulators

  arXiv (Cornell University) · 2026-04-15

  articleOpen access1st authorCorresponding

  Chern insulator systems are realizable in numerous physical systems and can support robust nonreciprocal transmission of energy. A routing functionality constructed from two counter-oriented Chern insulator regions, using coupled Haldane type systems is proposed. By adjusting the strength of a magnetic field and the frequency of an antenna source, it possible to steer the flow of energy: completely to the left, completely to the right, or split. Alternatively, two sources can be used to direct the flow of energy. This formulation has the potential to serve as a robust and reconfigurable component in optical transmission.

  PublisherOA PDF

• Spiral waves and localized modes in dispersive wave equations

  Wave Motion · 2025-05-25 · 1 citations

  article1st author
  PublisherDOI

• On the integrable six-wave interaction system and its space–time shifted reduction

  Physica D Nonlinear Phenomena · 2025-10-22

  article1st authorCorresponding
  PublisherDOI

• Integrable fractional Burgers hierarchy

  Journal of Nonlinear Waves · 2025-01-01 · 1 citations

  articleOpen access1st author

  Abstract Linear and integrable non-linear fractional evolution equations are discussed. Earlier results for the integrable fractional Korteweg–deVries (KdV) equation and the KdV hierarchy are reviewed. Using these as a guide, the fractional integrable Burgers equation and hierarchy and its solutions are analysed. Some explicit solutions are provided.

  PublisherOA PDFDOI

• Spiral Wave Solutions in Water Waves

  ArXiv.org · 2025-10-24

  preprintOpen access1st authorCorresponding

  Spiral wave solutions are found in linear and weakly nonlinear irrotational water wave equations. These unsteady spiral waves evolve from suitable initial conditions; they are not induced by external forcing. In the linear case, a long-time asymptotic result is obtained via the method of stationary phase. The asymptotic approximation is found to be in good agreement with the exact solution and reveals hyperbolic spiral structure. Numerical simulations show that these spiral waves persist in the presence of weak nonlinearity. While spiral solutions are frequently found in excitable media governed by reaction-diffusion systems, they comprise a new class of interesting two space one time dimensional solutions in fundamental linear and nonlinear dispersive wave systems.

  PublisherOA PDFDOI

• Fractional integrable Toda lattice and hierarchy

  Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2025-05-01 · 1 citations

  article1st author

  A fractional extension of the integrable Toda lattice with decaying data on the line is obtained. Completeness of squared eigenfunctions of a linear discrete real tridiagonal eigenvalue problem is derived. This completeness relation allows nonlinear evolution equations expressed in terms of operators to be written in terms of underlying squared eigenfunctions and is related to a discretization of the continuous Schrödinger equation. The methods are discrete counterparts of continuous ones recently used to find fractional integrable extensions of the Korteweg–de Vries (KdV) and nonlinear Schrödinger (NLS) equations. Inverse scattering transform (IST) methods are used to linearize and find explicit soliton solutions to the integrable fractional Toda (fToda) lattice equation. The methodology can also be used to find and solve fractional extensions of a Toda lattice hierarchy.

  PublisherDOI

• Fractional Integrable Dispersive Equations

  Nonlinear systems and complexity · 2024-01-01

  book-chapter1st author
  PublisherDOI

• Switching via wave interaction in topological photonic lattices

  Optics Letters · 2024-01-04 · 3 citations

  article1st authorCorresponding

  A honeycomb Floquet lattice with helically rotating waveguides and an interface separating two counter-propagating subdomains is analyzed. Two topologically protected localized waves propagate unidirectionally along the interface. Switching can occur when these interface modes reach the edge of the lattice and the light splits into waves traveling in two opposite directions. The incoming mode, traveling along the interface, can be adjusted and routed entirely or partially along either lattice edge with the switching direction based on a suitable mixing of the interface modes.

  PublisherDOI

• Inverse scattering transform for continuous and discrete space‐time‐shifted integrable equations

  Studies in Applied Mathematics · 2024-09-17 · 17 citations

  article1st authorCorresponding

  Abstract Nonlocal integrable partial differential equations possessing a spatial or temporal reflection have constituted an active research area for the past decade. Recently, more general classes of these nonlocal equations have been proposed, wherein the nonlocality appears as a combination of a shift (by a real or a complex parameter) and a reflection. This new shifting parameter manifests itself in the inverse scattering transform (IST) as an additional phase factor in an analogous way to the classical Fourier transform. In this paper, the IST is analyzed in detail for several examples of such systems. Particularly, time, space, and space‐time‐shifted nonlinear Schrödinger (NLS) and space‐time‐shifted modified Korteweg‐de Vries equations are studied. Additionally, the semidiscrete IST is developed for the time, space, and space‐time‐shifted variants of the Ablowitz–Ladik integrable discretization of the NLS. One‐soliton solutions are constructed for all continuous and discrete cases.

  PublisherDOI

Recent grants

• Collaborative Research: Mathematical and Computational Meghods for High-Performance Lightwave Systems

  NSF · $121k · 2005–2009

• Nonlinear Wave Motion

  NSF · $266k · 2013–2017

• Nonlinear Wave Motion

  NSF · $335k · 2009–2014

• Nonlinear Wave Motion

  NSF · $245k · 2017–2021

• Nonlinear Wave Motion

  NSF · $213k · 2003–2007

Frequent coauthors

• A. S. Fokas

  University of Cambridge

  62 shared

• Sarbarish Chakravarty

  University of Colorado Colorado Springs

  58 shared

• B. M. Herbst

  Stellenbosch University

  47 shared

• B. Prinari

  47 shared

• Ziad H. Musslimani

  Florida State University

  42 shared

• Javier Villarroel

  Universidad de Salamanca

  40 shared

• A. D. Trubatch

  Montclair State University

  40 shared

• C.M. Schober

  36 shared

Education

• Ph.D., Mathematics

  University of California, San Diego

  1974

• B.S., Mathematics

  University of California, San Diego

  1969

Awards & honors

• CU Distinguished Professor