Research

Research Areas:

• Nonlinear, dispersive Hamiltonian PDE (such as the b-CH and Novikov equations)

  • Orbital stability of smooth (solitary or periodic) traveling wave solutions 

  • Modulational (in)stability of smooth, periodic traveling wave solutions, with asymptotically small-amplitude (Novikov equation)

• Spectral (in)stability of periodic traveling wave solutions, with respect to two-dimensional transverse perturbations (Novikov-KP equation)

Peer-Reviewed Publications:

2) Orbital Stability of Smooth Solitary Waves in the Novikov Equation

With Mathew A. Johnson and Stephane Lafortune.

Journal of Nonlinear Science 34, 116, 2024. (Arxiv)

1) Orbital stability of periodic traveling waves in the b-Camassa–Holm equation

With Mathew A. Johnson.

Physica D , 461:134105, 2024. (Arxiv) 

Preprints:

2) Transverse Spectral Instability of the Novikov-KP Equation 

With Mathew A. Johnson, in preparation.

1) Modulational Instability of Small Amplitude Periodic Traveling Waves in the Novikov Equation

With Mathew A. Johnson and Stephane Lafortune, submitted. (Arxiv)

My advisor is Dr. Mathew A. Johnson, and his webpage is here: Website