Cauchy matrix scheme for semidiscrete lattice Korteweg–de Vries-type equations
Maebel Mesfun, Song‐lin Zhao
Abstract
Based on a determining equation set and master function, we consider a Cauchy matrix scheme for three semidiscrete lattice Korteweg–de Vries-type equations. The Lax integrability of these equations is discussed. Various types of solutions, including soliton solutions, Jordan-block solutions, and mixed solutions are derived by solving the determining equation set. Specifically, we find $$1$$ -soliton, $$2$$ -soliton, and the simplest Jordan-block solutions for the semidiscrete lattice potential Korteweg–de Vries equation.
Topics & Concepts
Korteweg–de Vries equationDispersionless equationMathematicsCauchy matrixLattice (music)SolitonMathematical physicsMatrix (chemical analysis)Lax pairMathematical analysisPhysicsIntegrable systemKadomtsev–Petviashvili equationPartial differential equationCharacteristic equationNonlinear systemQuantum mechanicsChemistryBoundary value problemChromatographyAcousticsCauchy boundary conditionFree boundary problemNonlinear Waves and SolitonsNonlinear Photonic SystemsAlgebraic structures and combinatorial models