Focusing and defocusing mKdV equations with nonzero boundary conditions: Inverse scattering transforms and soliton interactions

2020 ◽  
Vol 410 ◽  
pp. 132521 ◽  
Author(s):  
Guoqiang Zhang ◽  
Zhenya Yan
Keyword(s):  
Boundary Conditions ◽  
Inverse Scattering ◽  
Soliton Interactions ◽  
Nonzero Boundary ◽  
Scattering Transforms

Inverse scattering method for the Kundu-Eckhaus equation with zero/nonzero boundary conditions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Guixian Wang ◽  
Xiu-Bin Wang ◽  
Bo Han ◽  
Qi Xue
Keyword(s):  
Boundary Conditions ◽  
Inverse Scattering ◽  
Hilbert Problem ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Higher Order ◽  
Inverse Scattering Method ◽  
Scattering Method ◽  
Nonzero Boundary ◽  
Wave Phenomena

Abstract In this paper, the inverse scattering approach is applied to the Kundu-Eckhaus equation with two cases of zero boundary condition (ZBC) and nonzero boundary conditions (NZBCs) at infinity. Firstly, we obtain the exact formulae of soliton solutions of three cases of N simple poles, one higher-order pole and multiple higher-order poles via the associated Riemann-Hilbert problem (RHP). Moreover, given the initial data that allow for the presence of discrete spectrum, the higher-order rogue waves of the equation are presented. For the case of NZBCs, we can construct the infinite order rogue waves through developing a suitable RHP. Finally, by choosing different parameters, we aim to show some prominent characteristics of this solution and express them graphically in detail. Our results should be helpful to further explore and enrich the related nonlinear wave phenomena.

Sign in / Sign up

Export Citation Format

Share Document