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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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.