Selected Publications

We investigate the systematic generation of higher-order solitons and breathers of the Hirota equa- tion on different backgrounds. The Darboux transfor- mation is used to construct proper initial conditions for dynamical generation of high-intensity solitons and breathers of different orders on a uniform background. We provide expressions for the Lax pair generating functions and the procedure for calculating higher- order solutions when Jacobi elliptic functions are the background seed solutions of the Hirota equation. We confirm that the peak height of each soliton or breather in the nonlinear Darboux superposition adds linearly, to form the intensity maximum of the final solution.
Nonlin Dyn 89:1637–1649 (2017)

Recent Publications

  • Femtosecond laser induced structural dynamics and melting of Cu (111) single crystal: An ultrafast time-resolved x-ray diffraction study.

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  • Peak-height formula for higher-order breathers of the nonlinear Schrodinger equation on non-uniform backgrounds

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  • Systematic generation of higher-order solitons and breathers of the Hirota equation on different backgrounds

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  • Maximal intensity higher-order Akhmediev breathers of the nonlinear Schrödinger equation and their systematic generation

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  • Anatomy of the Akhmediev breather: Cascading instability, first formation time, and Fermi-Pasta-Ulam recurrence

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Teaching

I previously served as a TA for the following courses at Texas A&M Qatar:

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