2021•Communications in Theoretical PhysicsOpen access

Linear superposition of Wronskian rational solutions to the KdV equation

Wen‐Xiu Ma

Abstract

Abstract A linear superposition is studied for Wronskian rational solutions to the KdV equation, which include rogue wave solutions. It is proved that it is equivalent to a polynomial identity that an arbitrary linear combination of two Wronskian polynomial solutions with a difference two between the Wronskian orders is again a solution to the bilinear KdV equation. It is also conjectured that there is no other rational solutions among general linear superpositions of Wronskian rational solutions.

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Key concepts: Wronskian, Superposition principle, Korteweg–de Vries equation, Polynomial, Mathematics, Bilinear form, Bilinear interpolation, Applied mathematics