# Mathematical and Computational Nonlinear Physics

## Sample Projects

Deriving the Lax pair for the Hirota and Quintic nonlinear Schrödinger equations.

Studying the Fermi-Pasta-Ulam-Tsingou reccurence in the nonlinear Schrödinger equation.

Deriving doubly-periodic “Nonlinear Talbot Carpet” solutions and their possible applications in nonlinear optics.

Developing an experimentally feasible method for the systematic generation of higher-order breather solutions.

Sole developer and maintainer of the Julia package

`NonlinearSchrodinger.jl`

, implementing a variety of numerical algorithms and the Darboux transformation for the classically integrable nonlinear Schrödinger equation. [GitHub]

## Relevant Publications and Preprints

(2022). (2021). (2022).
Multi-elliptic rogue wave clusters of the nonlinear Schrödinger equation on different backgrounds.

(2022).
*Nonlinear Dynamics*.
Breathers, solitons and rogue waves of the quintic nonlinear Schrödinger equation on various backgrounds.

(2019).
*Nonlinear Dynamics*.
Talbot carpets by rogue waves of extended nonlinear Schrödinger equations.

(2019).
*Nonlinear Dynamics*.
Anatomy of the Akhmediev breather: cascading instability, first formation time, and Fermi-Pasta-Ulam recurrence.

(2015).
*Physical Review E*.
Maximal intensity higher-order Akhmediev breathers of the nonlinear Schrödinger equation and their systematic generation.

(2016).
(2017).
(2017).
*Physics Letters A*.