36 citations · 109 across the 35 of their papers we have counts for
37 papers
Recurrent bifurcations of stability spectra for steep Stokes waves in a deep fluid
Sergey Dyachenko, Robert Marangell, Dmitry E. Pelinovsky
We study the modulational stability problem for the traveling periodic waves (called Stokes waves) in an infinitely deep fluid by using pseudo-differential operators in conformal v…
Instability of solutions in a degenerate reaction diffusion equation
R. Marangell, J. J. Wylie, B. H. Bradshaw-Hajek
We study the spectral stability of travelling and stationary front and pulse solutions in a class of degenerate reaction-diffusion systems. We characterise the essential spectrum o…
Selection of the ground state on a compact metric graph
Robert Marangell, Dmitry E. Pelinovsky
We show that the ground state in the Fisher--KPP model on a compact metric graph with Dirichlet conditions on boundary vertices is either trivial (zero) or nontrivial and strictly…
Detecting eigenvalues in a fourth-order nonlinear Schrödinger equation with a non-regular Maslov box
Mitchell Curran, Robert Marangell
We use the Maslov index to study the eigenvalue problem arising from the linearisation about solitons in the fourth-order cubic nonlinear Schrödinger equation (NLSE). Our analysis…
Shock selection in reaction--diffusion equations with partially negative diffusivity using nonlinear regularisation
Thomas Miller, Alexander K. Y. Tam, Robert Marangell +2
We consider a general reaction--nonlinear-diffusion equation with a region of negative diffusivity, and show how a nonlinear regularisation selects a shock position. Negative diffu…
Stability of asymptotic waves in the Fisher-Stefan equation
T. T. H. Bui, P. van Heijster, R. Marangell
We establish spectral, linear, and nonlinear stability of the vanishing and slow-moving travelling waves that arise as time asymptotic solutions to the Fisher-Stefan equation. Nonl…