An extended (2+1)-dimensional modified Korteweg–de Vries–Calogero–Bogoyavlenskii–Schiff equation: Lax pair and Darboux transformation
Li Cheng, Yi Zhang, Wen‐Xiu Ma
Abstract
Abstract The aim of this paper is to study an extended modified Korteweg–de Vries–Calogero–Bogoyavlenskii–Schiff (mKdV-CBS) equation and present its Lax pair with a spectral parameter. Meanwhile, a Miura transformation is explored, which reveals the relationship between solutions of the extended mKdV-CBS equation and the extended (2+1)-dimensional Korteweg–de Vries (KdV) equation. On the basis of the obtained Lax pair and the existing research results, the Darboux transformation is derived, which plays a crucial role in presenting soliton solutions. In addition, soliton molecules are given by the velocity resonance mechanism.
Topics & Concepts
Transformation (genetics)Lax pairKorteweg–de Vries equationMathematical physicsPhysicsMathematicsPure mathematicsIntegrable systemNonlinear systemChemistryQuantum mechanicsGeneBiochemistryNonlinear Waves and SolitonsAlgebraic structures and combinatorial modelsMolecular spectroscopy and chirality