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In the past

  • Macroscopic approach to the Relativistic Extended Thermodynamics. (2003-2005)
  • Direct and Inverse Scattering Theory of the matrix Zakharov-Shabat system with potentials vanishing at infinity. (2005-2010)
  • Development of a method ( based on Inverse Scattering Transform (IST) and matrix exponential) to get explicit solutions for some evolution equations such as matrix Nonlinear Schrödinger (mNLS), sine-Gordon and modified Korteweg-de Vries equations. (2006-2010)
  • Time dependent scattering theory of the matrix Zakharov-Shabat system, in analogy to the time dependent scattering theory in quantum mechanics. (2007-2010)


  • Direct and Inverse Scattering Theory of the discrete Zakharov-Shabat system. (with C. van der Mee)
  • Exact solutions to the Integrable Discrete Nonlinear Schrödinger system (IDNLS system) by using the IST and Marchenko equations. (with C. van der Mee)
  • Explicit solutions of the defocusing NLS equations with boundary nonvanishing conditions. (with B. Prinari, C. van der Mee and F. Vitale)
  • Closed form solutions to the Camassa-Holm equation. (with T. Aktosun and C. van der Mee)
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