5 papers
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…
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…
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…