42 citations · 78 across the 10 of their papers we have counts for
10 papers
Well-posedness for the -problem relevant to the AKNS spectral problem
Junyi Zhu, Huan Liu
The well-posedness for the Dbar problem associated with the AKNS spectral problem is considered. In general, the relevant Dbar equation with normalization condition is quivalent to…
Dbar-approach to coupled nonlocal NLS equation and general nonlocal Reduction
Xueru Wang, Junyi Zhu
The coupled nonlocal NLS equation is studied by virtue of the Dbar-problem. Two spectral transform matrices are introduced to define two associated Dbar-problems. The re…
Inverse scattering transform for the Tzitzéica equation
Linlin Wang, Junyi Zhu
The inverse scattering transform is extended to investigate the Tzitzéica equation. A set of sectionally analytic eigenfunctions and auxiliary eigenfunctions are introduced. We not…
Dbar dressing method to nonlinear Schrödinger equation with nonzero boundary conditions
Junyi Zhu, Xueling Jiang, Xueru Wang
The Dbar dressing method is extended to study the focusing/defocusing nonlinear Schrödinger (NLS) equation with nonzero boundary condition. A special type of complex function is co…
Kuznetsov-Ma solution and Akhmediev breather for TD equation
Junyi Zhu, Linlin Wang
We present the inverse scattering transform for the TD equation, which is related to the Heisenberg spin equation. We note that the TD equation is an integrable model with high non…
Line-soliton and rational solutions to (2+1)-dimensional Boussinesq equation by Dbar-problem
Junyi Zhu
We present a generalized (2+1)-dimensional Boussinesq equation, including two cases which are called the plus Boussinesq equation and the minus one. To investigate these equations,…
Dressing by regularization to the Gerdjikov-Ivanov equation and the higher-order soliton
Juanjuan Yang, Junyi Zhu, Linlin Wang
Higher-order solitons, as well as simple -soliton solutions, of the Gerdjikov-Ivanov equation are derived by the dressing method based on the technique of regularization. By the…
Cusp solitons to the long-short waves equation and the -dressing method
Junyi Zhu, Yonghui Kuang
The dressing method based on matrix -problem is extended to study the long-short waves equation with the cases . The soliton solutions for the lo…
The discrete mKdV equation revisited: a Riemann-Hilbert approach
Junyi Zhu, Xianguo Geng, Yonghui Kuang
We study the plus and minus type discrete mKdV equation. Some different symmetry conditions associated with two Lax pairs are introduced to derive the matrix Riemann-Hilbert proble…
The AB equations and the -dressing method in semi-characteristic coordinates
Junyi Zhu, Xianguo Geng
The dressing method based on the matrix -problem is generalized to study the canonical form of AB equations. The soliton solutions for the AB equations are…