A polynomial conjecture connected with rogue waves in the KdV equation
Wen‐Xiu Ma
Abstract
A polynomial conjecture, associated with rational solutions including rogue wave solutions of the KdV equation, is presented. The conjecture can be used to show that for the bilinear KdV equation, an arbitrary linear combination of two Wronskian polynomial solutions with a difference two between the Wronskian orders will again be a solution.
Topics & Concepts
WronskianKorteweg–de Vries equationConjectureMathematicsPolynomialBilinear interpolationRogue waveBilinear formPure mathematicsMathematical analysisNonlinear systemPhysicsQuantum mechanicsStatisticsNonlinear Waves and SolitonsNonlinear Photonic SystemsAlgebraic structures and combinatorial models