Characterization of rational solutions of a KdV-like equation
Brian D. Vasquez Campos
Abstract
We characterize the rational solutions to a KdV-like equation which are generated from polynomial solutions to the corresponding generalized bilinear equation. We use a particular class of polynomials satisfying a quadratic difference equation to obtain that there are no solutions of the bilinear equation with degree (in the spatial variable) greater than 5. As a byproduct, we answer positively a conjecture of Yi Zhang and Wen-Xiu Ma about these solutions.
Topics & Concepts
Korteweg–de Vries equationMathematicsConjectureBilinear interpolationPolynomialBilinear formQuadratic equationVariable (mathematics)Class (philosophy)Characterization (materials science)Pure mathematicsApplied mathematicsDegree (music)Riccati equationRational functionMathematical analysisPartial differential equationPhysicsComputer scienceGeometryNonlinear systemArtificial intelligenceAcousticsOpticsStatisticsQuantum mechanicsNonlinear Waves and SolitonsAdvanced Differential Equations and Dynamical SystemsNumerical methods for differential equations