Matrix integrable fifth-order mKdV equations and their soliton solutions
Wen‐Xiu Ma
Abstract
We consider matrix integrable fifth-order mKdV equations via a kind of group reductions of the Ablowitz–Kaup–Newell–Segur matrix spectral problems. Based on properties of eigenvalue and adjoint eigenvalue problems, we solve the corresponding Riemann–Hilbert problems, where eigenvalues could equal adjoint eigenvalues, and construct their soliton solutions, when there are zero reflection coefficients. Illustrative examples of scalar and two-component integrable fifth-order mKdV equations are given.
Topics & Concepts
Integrable systemEigenvalues and eigenvectorsScalar (mathematics)SolitonMathematicsOrder (exchange)Mathematical physicsMatrix (chemical analysis)Mathematical analysisPure mathematicsPhysicsQuantum mechanicsNonlinear systemFinanceMaterials scienceEconomicsGeometryComposite materialNonlinear Waves and SolitonsNonlinear Photonic SystemsAlgebraic structures and combinatorial models