Four super integrable equations: nonlocal symmetries and applications
Hanyu Zhou, Kai Tian, Nianhua Li
Abstract
Abstract By applying Hamiltonian operators to gradients of spectral parameters, nonlocal symmetries quadratically depending on eigenfunctions of linear spectral problems are constructed for super bi-Hamiltonian equations including a super modified Korteweg–de Vries (KdV) equation, a super K (−1, −2) equation, Kupershmidt’s super KdV equation and a super Ablowitz–Kaup–Newell–Segur system. In each example, the nonlocal symmetry is prolonged to an enlarged system, and generates a finite symmetry transformation. On this basis, a non-trivial solution, as well as a Bäcklund transformation, is established for the each super equation under consideration.
Topics & Concepts
Korteweg–de Vries equationIntegrable systemHomogeneous spaceEigenfunctionMathematicsHamiltonian (control theory)Mathematical physicsHamiltonian systemSymmetry (geometry)Transformation (genetics)Quadratic growthMathematical analysisEigenvalues and eigenvectorsPhysicsNonlinear systemQuantum mechanicsGeometryGeneChemistryBiochemistryMathematical optimizationNonlinear Waves and SolitonsNonlinear Photonic SystemsMolecular spectroscopy and chirality