14 problems

Consider the three-dimensional parameter space $\mathbb R^2_{B,A}\times(\mathbb R_+)_{\omega}$. For $r\in\mathbb Z_{\neq0}$, the growth points of the phase-lock areas form the $r$-…

Nonexistence conjecture. For the case $N_{I}=1$, there are no nontrivial periodic stable solutions.

Real spectral-curve component conjecture. The following assertions hold:

Connectivity conjecture. The intersection $L_r^+\cap\Lambda_r$ coincides with the ray $S_r$, and therefore is connected.

Let $a$ be the parameter on the positive $a$-axis $(\mathbb R_+)_a$, let $\omega$ be the corresponding parameter on $(\mathbb R_+)_\omega$, and let $L_\ell$ denote the phase-lock a…

Let $\beta_{\ell,k}=(0,s_{\ell,k})$ be the points on the $s$-axis, where $s_{\ell,1},s_{\ell,2},\dots$ are the positive zeros of the Bessel function $J_\ell$, and let…

For every $\ell\in\mathbb Z_{\neq 0}$, let $\Lambda_\ell=\{B=\ell\omega\}$ and let $L_\ell^+=L_\ell\cap\{A>0\}$. If $\mathcal P_\ell=(\ell\omega,A(\mathcal P_\ell))$ is the higher…

Consider the two families of simple semirotors for the Josephson-junction system, consisting of two blocks of $k$ and $N-k$ identical junctions, with one block following a $T$-peri…

For positive integers $l,M,N$ with $lM=N$, an $(l,M,N)$-SWFS is a running solution with $M$ clusters of $l$ junctions, whose junction phases are time-shifted copies of one running…

Let the potential be the multidimensional washboard potential for a current-biased two-dimensional Josephson-junction array with frustration, and let $\beta_c$ denote the inertial…

The nonlocal double sine-Gordon equation models a Josephson layered structure whose current-phase relation contains two sine harmonics. The model admits particular velocities at wh…

Consider a long Josephson junction with a phase difference $\phi$ and a nontrivial ground state, whose eigenfrequency is the natural frequency of that ground state. Under microwave…

A spatially inhomogeneous sine-Gordon equation with a time-periodic drive models a microwave-driven long Josephson junction with phase shifts. The junction may have a spatially non…

Consider the free constant problem parameters of the reduced double confluent Heun equation associated with the overdamped Josephson junction equation, subject to the phase-lock co…