Higher Dimensional Camassa–Holm Equations
Sen‐Yue Lou, Man Jia, Xiazhi Hao
Abstract
Utilizing some conservation laws of the (1+1)-dimensional Camassa–Holm (CH) equation and/or its reciprocal forms, some (n+1)-dimensional CH equations for n ≥ 1 are constructed by a modified deformation algorithm. The Lax integrability can be proven by applying the same deformation algorithm to the Lax pair of the (1+1)-dimensional CH equation. A novel type of peakon solution is implicitly given and expressed by the LambertW function.
Topics & Concepts
PeakonLax pairConservation lawCamassa–Holm equationReciprocalDeformation (meteorology)Function (biology)Type (biology)MathematicsMathematical analysisMathematical physicsApplied mathematicsIntegrable systemPhysicsGeologyLinguisticsMeteorologyPaleontologyBiologyPhilosophyEvolutionary biologyNonlinear Waves and SolitonsNonlinear Photonic SystemsQuantum Mechanics and Non-Hermitian Physics