31 problems

Genuine nonlinear quantum-map conjecture. If Newtonian dynamics is more general than Hamiltonian dynamics, then genuine nonlinear quantum maps should exist, and nonlinear Schröding…

Let $f\colon\operatorname{int}(\mathbb{R}^n_+)\to\operatorname{int}(\mathbb{R}^n_+)$ be nonexpansive with respect to Thompson's part metric, and let $\tau_n$ denote the optimal uni…

Interpretive conjecture. A viable interpretation of EQM may be that, while linear QM is the fundamental theory of simple systems, EQM describes relatively isolated systems in this…

Previous-visits conjecture. To predict the next step in a time series, a good indication should come from the previous visits the system had made to the phase-space neighborhood co…

Nonlinear saturation conjecture. The resulting phase coherence will lead to a nonlinear amplitude saturation which will stop the wave predicted by the theory, and this will in turn…

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…

Independence conjecture. The nonlinearity of the phenomenon is not related to the linearity of the nondissipative phenomenon. This claim concerns the distinction between nonlineari…

Stochastic-driven nonlinear dynamical systems (SDNDSs) are used as solvers for combinatorial optimization, with graph connectivity affecting the number of terms in the cost functio…

The network dynamics use a pumping rate and may involve numerical integration with complex-valued variables. Synchronization-delay conjecture. The synchronization of the network ma…

Let a one-dimensional disordered Klein–Gordon-type or disordered nonlinear Schrödinger-type chain be in the atomic limit, with an initially localized wave packet and finite initial…

Let $\mathcal{C}$ be the upper cell order, and let the reaction rates be constant choices of the parameters entering the steady-state equations. A solution is physical when the cor…

Let $\Omega\subset\mathbb{R}$ be a bounded domain, let $m$ be non-negative and bounded, and consider the Neumann problem … … with positive initial data and the boundary conditions…

Unstable nonlinear wave mode conjecture. This onset of supratransmission is due to the excitation of an unstable nonlinear wave mode of the system.

The Fermi–Pasta–Ulam–Tsingou lattice exhibits near-recurrence of its original configuration on a relatively short time scale. FPUT conjecture. Subsequent behavior at each such peri…

Let $\{({\boldsymbol{x}}_k^\star,{\boldsymbol{u}}_k^\star,{\boldsymbol{\lambda}}_k^\star)\}_k$ be the primal-dual trajectory of a nonlinear optimal control problem, where…

Stabilizability-regularization conjecture. Using stabilizability constraints as a form of regularization should prune the hypothesis space in a task-tailored manner, resulting in m…

A continuous spectrum is a continuous range of observed frequencies, as occurs in nonlinear systems such as the Duffing oscillator; Koopman models may use deep neural networks (DNN…

Consider a nonlinear autonomous system … whose second-order form is … so that the functions $g_i$ act as oscillator frequencies and the functions $h_i$ are the remaining terms. Com…

Let $\mathcal G$ be a graph of the fourth kind, meaning a graph with no terminal point, no cycle covering, and more than one half-line, and suppose that…

Endpoint behavior conjecture. There exists $E_k>0$ such that if

Let $m,n$ be the mode indices, let $P$ be the parameter, and define … Let $\Theta_m$ and $\Theta_n$ be the corresponding modes with energy $E_{\Theta_m}$. Assume … Let $E_1$ and…

Let $m,n$ be the mode indices, let $P$ be the parameter, and let $\Theta_m$ and $\Theta_n$ denote the corresponding modes with energy $E_{\Theta_m}$. Assume … Let $E_2$ be the thre…

All-energy stability conjecture. Under these assumptions, $\Theta_m$ is linearly stable with respect to $\Theta_n$ for every $E_{\Theta_m}>0$.

Diffusive propagation conjecture. A similar behavior is expected for the deterministic nonlinear Hamiltonian dynamics corresponding to an interaction of the type…

Let $({\cal P}_0)$ be the discretized nonlinear algebraic problem associated with a nonlinear dynamical system, and let $({\cal P})$ be the corresponding optimization problem with…