Analyzes transition asymptotics for real solutions of the sinh-Gordon Painlevé III equation, mapping exponential to elliptic to trigonometric regimes via the scaling |p|^2 = 1 + e^{2ϰ x}.
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nlin.SI 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
The Gurevich-Pitaevskii solution to KdV, known to satisfy a self-similar reduction from the next hierarchy member, must obey a first-order PDE if any lower-order one and admits a converging Laurent series in x and t.
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Transition asymptotics for the real solutions of the sinh-Gordon Painlev\'e III equation
Analyzes transition asymptotics for real solutions of the sinh-Gordon Painlevé III equation, mapping exponential to elliptic to trigonometric regimes via the scaling |p|^2 = 1 + e^{2ϰ x}.
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On the Gurevich-Pitaevskii solution of KdV
The Gurevich-Pitaevskii solution to KdV, known to satisfy a self-similar reduction from the next hierarchy member, must obey a first-order PDE if any lower-order one and admits a converging Laurent series in x and t.