The focusing Manakov system with nonzero boundary conditions

Nonlinearity ◽  
2015 ◽  
Vol 28 (9) ◽  
pp. 3101-3151 ◽  
Author(s):  
Daniel Kraus ◽  
Gino Biondini ◽  
Gregor Kovačič
Keyword(s):  
Boundary Conditions ◽  
Nonzero Boundary

N-soliton solution for a higher-order Chen–Lee–Liu equation with nonzero boundary conditions

2019 ◽  
Vol 34 (04) ◽  
pp. 2050054 ◽  
Author(s):  
Yi Zhao ◽  
Engui Fan
Keyword(s):  
Boundary Conditions ◽  
Soliton Solution ◽  
Hilbert Problem ◽  
Asymptotic Properties ◽  
Soliton Solutions ◽  
Higher Order ◽  
Third Order ◽  
Third Order Dispersion ◽  
Nonzero Boundary ◽  
Riemann Hilbert Problem

In this paper, the Riemann–Hilbert approach is applied to investigate a higher-order Chen–Lee–Liu equation with third-order dispersion and quintic nonlinearity terms. Based on the analytical, symmetric and asymptotic properties of eigenfunctions, a generalized Riemann–Hilbert problem associated with Chen–Lee–Liu equation with nonzero boundary conditions is constructed. Further, the [Formula: see text]-soliton solution is found by solving the generalized Riemann–Hilbert problem. As an illustrative example, two kinds of one-soliton solutions with different forms of parameters are obtained.

The multi-triple-pole solitons for the focusing mKdV hierarchy with nonzero boundary conditions

2021 ◽  
pp. 2150483
Author(s):  
Weifang Weng ◽  
Zhenya Yan
Keyword(s):  
Boundary Conditions ◽  
Soliton Solutions ◽  
Mkdv Equation ◽  
Scattering Coefficients ◽  
Dark Solitons ◽  
Scattering Transform ◽  
Nonzero Boundary ◽  
Trace Formulae ◽  
Fifth Order ◽  
Mkdv Hierarchy

In this paper, the general triple-pole multi-soliton solutions are proposed for the focusing modified Korteweg–de Vries (mKdV) equation with both nonzero boundary conditions (NZBCs) and triple zeros of analytical scattering coefficients by means of the inverse scattering transform. Furthermore, we also give the corresponding trace formulae and theta conditions. Particularly, we analyze some representative reflectionless potentials containing the triple-pole multi-dark-anti-dark solitons and breathers. The idea can also be extended to the whole mKdV hierarchy (e.g. the fifth-order mKdV equation, and third-fifth-order mKdV equation) with NZBCs and triple zeros of analytical scattering coefficients. Moreover, these obtained triple-pole solutions can also be degenerated to the triple-pole soliton solutions with zero boundary conditions.

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