6 problems

Let the $J$-bF equation be the higher-order $b$-family equation denoted by. A $b$-dependent peakon is a real peaked travelling-wave solution whose parameters depend on $b$. The $b$…

Let the $J$-bF equation be the higher-order $b$-family equation denoted by, with wave speed $c$ and constants $a_i$. A $b$-independent peakon is a peaked travelling-wave solution w…

Let $\mathcal{S}_{\mathrm{ext}}(N)$ be the extended spectral data for an $N$-peakon NV2 system, let $\mathcal{S}(N)$ be the actual spectral data set, and let $\Lambda_2(N)$ be the…

Positivity conjecture. For spectral data $\{\lambda_k,\mathbf{b}_k\}_{k=1}^N\in\mathcal{S}(N)$, all determinants in these conditions are positive. These inequalities would show tha…

The multipeakon NV2 system has spectral data consisting of eigenvalues and vector weights, and its actual spectral data set is a subset of the extended spectral data set. A matrix…

Consider the cross-coupled peakon equations with $n_1+n_2$ particles of one type and $n_1$ particles of the other type, where $n_1,n_2\in\mathbb{N}$. A long-time chain formation co…