The bound-state soliton solutions of the complex modified KdV equation
Yongshuai Zhang, Xiangxing Tao, Shuwei Xu
Abstract
Abstract The inverse scattering method is performed to the complex modified Korteweg–de Vries equation with zero boundary condition by developing an appropriate Riemann–Hilbert problem (RHP). We solve the RHP when reflection coefficient has multiple higher-order poles, and display the formulae of bound-state (BS) solitons and multiple BS solitons which correspond to one higher-order pole and multiple higher-order poles, respectively. The patterns of the BS solitons are shown and the interactions between solitons and BS solitons are considered.
Topics & Concepts
MathematicsKorteweg–de Vries equationSolitonInverse scattering problemBound stateRiemann–Hilbert problemMathematical analysisBoundary (topology)State (computer science)InverseUpper and lower boundsMathematical physicsInverse problemBoundary value problemOrder (exchange)Nonlinear systemQuantum mechanicsGeometryPhysicsAlgorithmEconomicsFinanceNonlinear Waves and SolitonsNonlinear Photonic SystemsAdvanced Mathematical Physics Problems