The modified Camassa–Holm equation: Bäcklund transformation and nonlinear superposition formula*
Gaihua Wang, Q.P. Liu, Hui Mao
Abstract
Abstract This paper is concerned with the modified Camassa–Holm equation and its Bäcklund transformation. With the aid of reciprocal transformation and the associated modified Camassa–Holm equation, a Bäcklund transformation, which involves both dependent and independent variables, is constructed for the modified Camassa–Holm equation. The related nonlinear superposition formula is worked out and applications of both Bäcklund transformation and nonlinear superposition formula are considered.
Topics & Concepts
Camassa–Holm equationMathematicsTransformation (genetics)Superposition principleNonlinear systemMathematical physicsMathematical analysisPhysicsIntegrable systemChemistryQuantum mechanicsGeneBiochemistryNonlinear Waves and SolitonsNonlinear Photonic SystemsAlgebraic structures and combinatorial models