Soliton molecules and dynamics of the smooth positon for the Gerdjikov–Ivanov equation*
Xiangyu Yang, Zhao Zhang, Biao Li
Abstract
Soliton molecules are firstly obtained by velocity resonance for the Gerdjikov–Ivanov equation, and n -order smooth positon solutions for the Gerdjikov–Ivanov equation are generated by means of the general determinant expression of n -soliton solution. The dynamics of the smooth positons of the Gerdjikov–Ivanov equation are discussed using the decomposition of the modulus square, the trajectories and time-dependent “phase shifts” of positons after the collision can be described approximately. Additionally, some novel hybrid solutions consisting solitons and positons are presented and their rather complicated dynamics are revealed.
Topics & Concepts
SolitonPhysicsDynamics (music)Resonance (particle physics)Square (algebra)Phase (matter)MoleculeMathematical physicsOrder (exchange)ModulusMathematical analysisQuantum mechanicsMathematicsNonlinear systemGeometryEconomicsAcousticsFinanceNonlinear Waves and SolitonsAdvanced Fiber Laser TechnologiesNonlinear Photonic Systems