Double and triple poles solutions for the Gerdjikov-Ivanov type of derivative nonlinear Schrödinger equation with zero/nonzero boundary conditions
arXiv:2104.12073 · doi:10.1063/5.0061807
Abstract
In this work, the double and triple poles soliton solutions for the Gerdjikov-Ivanov(GI) type of derivative nonlinear Schrödinger equation with zero boundary conditions(ZBCs) and nonzero boundary conditions(NZBCs) are studied via Riemann-Hilbert (RH) method. Though spectral problem analysis, we first give out the Jost function and scattering matrix under ZBCs and NZBCs. Then according to the analyticity, symmetry and asymptotic behavior of Jost function and scattering matrix, the Riemann-Hilbert problem(RHP) with ZBCs and NZBCs are constructed. Further, the obtained RHP with ZBCs and NZBCs can be solved in the case that reflection coefficients have double or triple poles. Finally, we derive the general precise formulae of N-double and N-triple poles solutions corresponding to ZBCs and NZBCs, respectively. The dynamical behaviors for these solutions are further discussed by image simulation.
References in corpus (9)
- The Rogue Wave and breather solution of the Gerdjikov-Ivanov equation
- The higher order Rogue Wave solutions of the Gerdjikov-Ivanov equation
- General soliton matrices in the Riemann-Hilbert problem for integrable nonlinear equations
- Inverse scattering transforms and N-double-pole solutions for the derivative NLS equation with zero/non-zero boundary conditions
- Long-time asymptotic for the derivative nonlinear Schrödinger equation with decaying initial value
- Inverse scattering transform of an extended nonlinear Schrödinger equation with nonzero boundary conditions and its multisoliton solutions
- The Riemann-Hilbert approach to focusing Kundu-Eckhaus equation with nonzero boundary conditions
- Inverse scattering transform and soliton solutions for the modified matrix Korteweg-de Vries equation with nonzero boundary conditions
- Dressing by regularization to the Gerdjikov-Ivanov equation and the higher-order soliton