• Sloan Fellowship, 1975—1977.
• Clarkson Graham Research Award, 1976.
• John Simon Guggenheim Foundation Fellowship, 1984.
• National Academy of Sciences Symposium on Soliton Theory Kiev, USSR 1979.

Books

• Solitons and the Inverse Scattering Transform, M.J. Ablowitz and H. Segur, (SIAM Studies in Applied Mathematics) 1981

• Topics in Soliton Theory and Exactly Solvable Nonlinear Equations, Eds. M.J. Ablowitz, B. Fuchssteiner and M.D. Kruskal, (World Scientific) 1987

• Solitons, Nonlinear Evolution Equations and Inverse Scattering, M.J. Ablowitz and P.A. Clarkson, (London Mathematical Society Lecture Notes Series, 516 pages, (Cambridge University Press, Cambridge, UK, 1991)

• Complex Variables: Introduction and Applications, Mark J. Ablowitz and A.S. Fokas, (Cambridge University Press, Cambridge, UK, 1997)

• Nonlinear Physics: Theory and Experiment. II, M.J. Ablowitz, M. Boiti, F. Pempinelli and B. Prinari, (World Scientific 2003)

• Discrete and Continuous Nonlinear Schrödinger Systems, Mark J. Ablowitz, B. Prinari and D. Trubatch, M. J. Ablowitz B. Prinari and A. D. Trubatch, 258 (Cambridge University Press, Cambridge, UK, 2004)