10 problems

Consider the complex Ginzburg–Landau equation with parameter $\theta=\pi/2$, namely the nonlinear Schrödinger equation. A solution is unbounded if its norm becomes arbitrarily larg…

Infinite-period saddle-node boundary conjecture. The saddle-node line for $P\to\infty$ provides a lower boundary for the transition from phase to defect chaos in the one-dimensiona…

Inter-peak-spacing conjecture. Defects occur if and only if $p>P_{SN}$.

Defect-density conjecture. Defects arise when $p>P_{SN}$, and consequently

Divergent-MAW-period boundary conjecture. The $P_{SN}\to\infty$ limit is a lower boundary for the transition from phase chaos to defect chaos.

Phase-chaos persistence conjecture. Phase chaos persists in the thermodynamic limit in this regime.

Branch-counting conjecture. The supercritical CGL equation has a countable number of branches of nontrivial radial self-similar singular solutions. These branches can be labeled by…

Let $u_1$ be the nontrivial equilibrium of the complex Ginzburg–Landau equation, and let $\theta\in[-\pi/2,\pi/2]$. The strong unstable manifold is the $(1$-complex-dimensional$)$…

Let $\mathcal L(t)$ be the time-periodic operator obtained by linearizing the cubic-quintic complex Ginzburg–Landau equation about a periodically stationary solution, let…

In the continuous locally coupled complex Ginzburg–Landau equation, consider a frozen vortex chimera with a coherent spiral domain, an incoherent amplitude-turbulent domain, and an…