7 problems

Let a soliton-bearing system be perturbed by an ac force, and suppose that the soliton or solitary wave under consideration has no resonances with other modes intrinsic to the exci…

Let $F(u)=1-\cos(u)$, so that the variable-coefficient sine-Gordon equation is a perturbation of … and let the coefficients satisfy the conditions denoted by. The kink is the stati…

Physical asymptotic approximation conjecture. In the regime $\lambda_1\ll\lambda_3$, the dynamics can be described by the Sine–Gordon equation, while in the regime…

Let $\rho(t)$ be the spatial shift appearing in the asymptotic description of a sine-Gordon kink solution with initial data in the energy space. Convergence conjecture. Under some…

Let $\hat{H}_{SG}$ be the sine-Gordon Hamiltonian, let $\hat{\Upsilon}$ be any intertwiner identified above, and let $\lambda$ be an eigenvalue of $\hat{H}_{SG}$. A Darboux operato…

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…