Cauchy matrix approach to the noncommutative Kadomtsev–Petviashvili equation with self-consistent sources
Zhihao Shi, Shangshuai Li, Da‐jun Zhang
Abstract
We develop a direct method, the Cauchy matrix approach, to construct matrix solutions of noncommutative soliton equations. This approach is based on the Sylvester equation, and solutions can be presented without using quasideterminants. The matrix Kadomtsev–Petviashvili equation with self-consistent sources is employed as an example to demonstrate the approach. As a reduction, explicit solutions of the matrix Mel’nikov model for long–short wave interaction are obtained.
Topics & Concepts
Noncommutative geometryMathematicsCauchy distributionMathematical physicsMatrix (chemical analysis)Kadomtsev–Petviashvili equationSelf consistentPure mathematicsMathematical analysisPhysicsQuantum electrodynamicsCharacteristic equationPartial differential equationMaterials scienceComposite materialAlgebraic structures and combinatorial modelsAdvanced Algebra and GeometryNoncommutative and Quantum Gravity Theories