Tropicalization of an algebraic differential equation bounds the t-adic orders of its formal Hahn series solutions by the orders of elementary k-solutions to the tropical equation.
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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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Elementary solutions of ordinary tropical differential equations, and vanishing orders of solutions of algebraic differential equations
Tropicalization of an algebraic differential equation bounds the t-adic orders of its formal Hahn series solutions by the orders of elementary k-solutions to the tropical equation.