Developed, with colleagues Whitehead, Cross, Passot, Ercolani, envelope and modulation equations describing the behaviors of pattern order parameters.
Using the self-induced transparency of optical pulses in inhomogeneously broadened media as a paradigm, he have investigated the dependence of the Anderson localization distance on wave amplitude and shape.
With L’vov, investigated the role of finite flux (rather than Fermi-Dirac) equilibria of the fermionic quantum kinetic equation in enhancing laser output.
Developed (with Nazarenko, Biven, Connaughton) conditions on the wavenumber ranges of validity of the Kolmogorov-Zakharov (KZ) spectra in order for the wave turbulence closure to hold.
Developed with colleagues (Nazarenko, Rubenchik, Zakharov) useful results in connection with the use of nonlinear plasma properties to enhance communication with reentry space vehicles.
With Benno Rumpf, have developed an explanation for the appearance of robust, large and coherent structures in nonintegrable systems with modulational (self-focusing) instabilities and constrained by more than one conservation law.