Two super Camassa–Holm equations: Reciprocal transformations and applications
Kai Tian, Q.P. Liu, Wen Yue
Abstract
Reciprocal transformations are introduced for two super Camassa–Holm (CH) equations. Under these transformations and appropriate changes of dependent variables, the super CH equation, proposed by Geng et al. [Stud. Appl. Math. 130, 1 (2013)], is converted to a negative member of the super Korteweg–de Vries (KdV) hierarchy studied by Geng and Wu in 2010 [Appl. Math. Lett. 23, 716 (2010)], while the other super CH equation, due to Zhang and Zuo [J. Math. Phys. 52, 073503 (2011)], is related to a new super KdV hierarchy. In the latter case, algebraic properties of this new super KdV hierarchy are established, including Hamiltonian operators, a recursion operator, and conserved quantities.
Topics & Concepts
Korteweg–de Vries equationMathematicsKdV hierarchyReciprocalHierarchyOperator (biology)Hamiltonian (control theory)Mathematical physicsConserved quantityAlgebraic numberPure mathematicsAlgebra over a fieldMathematical analysisPhysicsNonlinear systemQuantum mechanicsBiochemistryTranscription factorRepressorChemistryMarket economyMathematical optimizationGeneEconomicsLinguisticsPhilosophyNonlinear Waves and SolitonsAlgebraic structures and combinatorial modelsNonlinear Photonic Systems