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.
Phase Shift in the Whitham Zone for the Gurevich-Pitaevskii Special Solution of the Korteweg-de Vries Equation
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abstract
We get the leading term of the Gurevich-Pitaevskii special solution to the KdV equation in the oscillation zone without using averaging methods.
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nlin.SI 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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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.