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The long-time behavior of solutions to the initial value problem for theKorteweg-de Vries equation on the whole line, with general initial conditionshas been described uniformly using five different asymptotic forms. Four ofthese asymptotic forms were expected: the quiescent behavior (for |x| verylarge), a soliton region (in which the solution behaves as a collection ofisolated solitary waves), a self-similar region (in which the solution isdescribed via a Painlev\'e transcendent), and a similarity region (where thesolution behaves as a simple trigonometric function of the quantities t andx/t). A fifth asymptotic form, lying between the self-similar (Painlev\'e) andthe similarity one, has been described in terms of classical ellipticfunctions. An integral of elliptic type, giving an explicit representation ofthe phase, has appeared in this context. The same integral has appeared in thetable of integrals by Gradshteyn and Ryzhik. Our goal here is to confirm thevalidity of this entry.

Collisionless shock region of the KdV equation and an entry in Gradshteyn and Ryzhik