Rogue wave and lump patterns in several integrable equations are asymptotically predicted by the root distributions of Umemura polynomials associated with the third Painlevé equation.
±(N−1), then the the wave field asymptotically splits intoN(N+ 1)/2fundamental lumps u1(x−ˆx0, t− ˆt0), where(ˆx0, ˆt0)are given by Eq
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Rogue-wave and lump patterns associated with the third Painlev\'{e} equation
Rogue wave and lump patterns in several integrable equations are asymptotically predicted by the root distributions of Umemura polynomials associated with the third Painlevé equation.