The ∂-dressing method and soliton solutions for the three-component coupled Hirota equations
Z.M. Wang, Shou-Fu Tian, Jia Cheng
Abstract
The ∂̄-dressing method is developed to study the three-component coupled Hirota (tcCH) equations. We first start from a ∂̄-problem and construct a new spectral problem. Based on the recursive operator, we successfully derive the tcCH hierarchy associated with the given spectral problem. In addition, the soliton solutions of the tcCH equations are first obtained via determining the spectral transform matrix in the ∂̄-problem. Finally, one-, two-, and three-soliton solutions are analyzed to discuss the dynamic phenomena of the tcCH equations. It is remarked that the interaction between solitons depends on whether the characteristic lines intersect.
Topics & Concepts
SolitonMathematicsComponent (thermodynamics)HierarchyOperator (biology)Matrix (chemical analysis)Applied mathematicsConstruct (python library)Mathematical analysisPhysicsQuantum mechanicsNonlinear systemComputer scienceProgramming languageRepressorComposite materialTranscription factorBiochemistryMaterials scienceMarket economyEconomicsChemistryGeneNonlinear Waves and SolitonsNonlinear Photonic SystemsAlgebraic structures and combinatorial models