10 problems

A soliton solution is a solution constructed using Bäcklund transformations, and an attached Akhmediev breather is an Akhmediev breather attached to such a soliton solution. Instab…

As is typical for invasion into an unstable state, fronts may form with a continuous family of speeds. In a moving reference frame, the unstable state is absolutely unstable at low…

The focusing modified Korteweg–de Vries equation admits two families of periodic traveling waves, and spectral instability bands can exhibit figure-$8$ patterns, crossing at the im…

Let b\text{{\mathcal L_{\mu,\epsilon}}} be the linearized operator, let b\text{{\lambda_1^\pm(\mu,\epsilon)}} be its unstable eigenvalues, and let…

Consider the linearized water-wave operator at a small-amplitude Stokes wave, with Floquet exponent $b\text{{\mu}}$ and small amplitude parameter $b\text{{\epsilon}}$. Let…

Consider a solution consisting of traveling waves such that Condition … is satisfied. For sufficiently large $t$, assume the traveling waves separate so that the later-time instabi…

Let $m_{ij\ell}$ denote the coefficients in the right-hand side of the system \, and consider nonzero traveling wave profiles for that system. Generic instability conjecture. For…

Consider the autonomous Galerkin systems associated with the positive cubic beam problem, with Fourier modes $varphi_j$ and the notion of full instability defined by the two condit…

Consider solutions of the complex Burgers equation ${\rm (B)}_\varepsilon$ with initial data of amplitude $O(1)$ and frequencies $O(1/\varepsilon)$, of the form $a(x/\varepsilon)$.…

Consider statistical procedures that attempt to extract complex structure from data, with instability understood as extreme sensitivity of the resulting data map to small changes i…