9 problems

The tWhitham equation is a model for traveling water waves, and a traveling-wave solution has a wave height, with maximal height meaning the greatest height attained among such sol…

The two-bus power flow system uses the load parameter and the associated maximization formulation to identify a maximal saddle-node bifurcation point. Generalization conjecture. Th…

Source-type solution conjecture. This function is a source-type solution of the nonlinear time-fractional equation referred to as equation in the source.

The thermal temperature and the quantum temperature $T_\Psi$ are considered for a system with nonlinear coupling $b$. Temperature–coupling conjecture. Thermal temperature is relate…

Lieb–Yau conjecture. For each $N<N^*$, there exists a unique ground state (minimizer) of $e(N)$.

Let a nonlinear partial differential equation be discretized by a nonlinear numerical method, and let a consistent linearized form of that method be given. Linearization sufficienc…

Superprocess extension conjecture. To extend the application of superprocesses to more general nonlinear equations, one should move from processes on measures to processes on gener…

Existence and uniqueness conjecture. These equations have a unique real-valued solution $\varphi$ provided that

Let $U^{(l)}$ and $V_N^{(l)}$ be linear Lax operators built from the building blocks $\{\lambda,U^{(0)}\}$ and their $x$-derivatives, with scaling dimensions…