MathDB2 problems
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The asymptotic stability conjecture for SGN line solitary waves
Asymptotic stability conjecture. A perturbation of the line solitary wave leads, for sufficiently large times, to the unperturbed line solitary wave plus radiation.
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The defocusing conjecture for two-dimensional SGN solitary waves
Defocusing conjecture. There are no stable SGN solitary waves localized in two dimensions, and the equation has a defocusing effect.