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math.AP2021
High-frequency instabilities of the Ostrovsky equation
Bhavna, Atul Kumar, Ashish Kumar Pandey
We study spectral stability of small amplitude periodic traveling waves of the Ostrovsky equation. We prove that these waves exhibit spectral instabilities arising from a collision…
math.AP2017★ 3 cited
Comparison of modulational instabilities in full-dispersion shallow water models
Ashish Kumar Pandey
We study the modulational instability of a shallow water model, with and without surface tension, which generalizes the Whitham equation to include bi-directional propagation. With…
math.AP2017★ 1 cited
Modulational instability in the full-dispersion Camassa-Holm equation
Vera Mikyoung Hur, Ashish K. Pandey
We determine the stability and instability of a sufficiently small and periodic traveling wave to long wavelength perturbations, for a nonlinear dispersive equation which extends a…