One of my areas of interest is nonlinear dynamics. Here is a list of some of my works in this area.
Here is a model of an induction motor with quasiperiodic drive. I did this together with PRANAV, who was my junior in IITK. We completed this in June 2015. The journal reference is Journal of Applied Nonlinear Dynamics 6 (1), 57-77 (2017).
Motor with quasiperiodic
Here is a work done with MATTHEW DAVIDOW under Professor RAND's supervision. It deals with a singularity in a delayed differential equation. We completed this in January 2017. It has been accepted for publication in Nonlinear Dynamics.
Here is a basic but general model of shock wave propagation in linear medium with a travelling disturbance. A calculation of the appropriate GREEN's function leads to an exact formula for the wavefront in the cases where the disturbance is subsonic and supersonic. It also shows a phase reversal of the wave across the sound barrier. Unfortunately, a similar situation had already been considered by PHILIP MORSE and UNO INGARD in their book "Theoretical Acoustics," a fact which was brought to my attention by a reviewer for EPL. The technique that MORSE et. al. had used is completely different so this document still has some archival value.
Here is a first-principles model of the motion of a violin string which yields Helmholtz type limit cycles as a solution and also gives the regions of parameter space where this cycle exists and is stable. The small size of this region explains why the instrument is difficult to play. The journal reference is AIP Chaos 28 (8), 083116 (2018). See also Tutorial 125 in DELTA (my differential equations book) for a version with larger number of calculational steps but no literature review.