5 papers · 1 filter
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,…