6 problems

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The ABS model's no-conservation-laws conjecture
The $1+1$ -dimensional nonlinear Dirac equation admits $mathcal{PT}$ -symmetric perturbations, including the Alexeeva-Barashenkov-Saxena (ABS) model. A conservation law is a quanti…
Conjectureopennonlinear-dirac-equations pt-symmetry soliton-dynamicsarXiv posted 2 days ago
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Tzvetkov's small-data global existence conjecture for nonlinear Dirac equations
Tzvetkov's conjecture. The nonlinear Dirac equation has a small-data global solution when its nonlinearity takes such special forms as $N_{1}$ and $N_{2}$ . This conjecture concerns…
Conjectureopenglobal-existence nonlinear-dirac-equations null-formsarXiv posted 2 days ago
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Extension and disappearance of the nonlinear Dirac bifurcation branch below $-m$
Branch-extension conjecture. The branch should extend to the left of $-m$ into the spectrum and disappear at some point.
Conjectureopenbifurcation-theory nonlinear-dirac-equations spectral-gapsarXiv posted 2 days ago
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Uniqueness and symmetry conjecture for ground states of the three-dimensional limit equation
Let $\psi$ be a ground state solution of the limit equation … where $\lambda$ is the parameter in the equation and the Pauli matrices $\gamma_1,\gamma_2,\gamma_3$ are as defined in…
Conjectureopennonlinear-dirac-equations spinorial-geometry yamabe-problemarXiv posted 2 days ago
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Chadam–Glassey conjecture on deriving the Yukawa Dirac equation from Dirac–Klein–Gordon
Chadam–Glassey conjecture. The equation with Yukawa potential $V$ can be derived by uncoupling the Dirac–Klein–Gordon equations.
Conjectureopendirac-klein-gordon-equations hartree-equations nonlinear-dirac-equationsarXiv posted 2 days ago
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Global stability of large cubic Dirac solutions near the Lochak–Majorana condition
Global stability conjecture. Small perturbations of initial data satisfying the Lochak–Majorana condition give rise to global large solutions of the cubic Dirac equation. The Locha…
Conjectureopencubic-dirac-equation global-solutions nonlinear-dirac-equationsarXiv posted 2 days ago

6 problems

The ABS model's no-conservation-laws conjecture

Tzvetkov's small-data global existence conjecture for nonlinear Dirac equations

Extension and disappearance of the nonlinear Dirac bifurcation branch below −m-m−m

Uniqueness and symmetry conjecture for ground states of the three-dimensional limit equation

Chadam–Glassey conjecture on deriving the Yukawa Dirac equation from Dirac–Klein–Gordon

Global stability of large cubic Dirac solutions near the Lochak–Majorana condition

Extension and disappearance of the nonlinear Dirac bifurcation branch below $-m$