8 problems

The Adkins–Nappi model is a semilinear modification of the wave map equation describing a repulsive interaction involving meson fields. By finite energy smooth initial data, we mea…

Let the Skyrme model have domain $\mathbb S^3_\rho$ and let $x\mapsto x/\rho$ be the homothety, where $\rho>0$. Two maps are in the same homotopy class when they are homotopic as m…

The co-rotational Skyrme model is considered in spatial dimension $d=5$, with the profile from the paper's equation (ProfileU) and the scaling properties of the full equation. Blow…

In the Skyrme model, let $k$ denote the Skyrmion's baryon number, and call a massive or vibrational mode light when it belongs to the set of modes considered in the cited vibration…

Consider the two linked lines obtained as preimages of two distinct regular points on the 2-sphere under the Hopf map applied to a Skyrme field. The underlying field is an original…

Let $X=\mathbb{R}^3\cup\{\infty\}$ and let $U:X\to S^3$ be a map of degree $B$. Interpret $U$ as two vortices in $\psi_1$ and $\psi_2$ of $\boldsymbol{\psi}\in S^3$, with winding n…

The model admits soliton solutions, and BPS solitons are solutions whose energies saturate the BPS bound. All-solitons-BPS conjecture. All solitons are, in fact, BPS solitons. Nume…

Let $\psi^{\alpha}_{k,\ell}:\mathbb{S}^{3}\to\mathbb{S}^{3}$ be an equivariant $\alpha$-join, with $k,\ell\in\mathbb{Z}^{*}$, $\alpha(0)=0$, and $\alpha(\pi/2)=\pi/2$. Its degree i…