Communications in Theoretical Physics ( IF 3.1 ) Pub Date : 2021-02-25 , DOI: 10.1088/1572-9494/abdeac Cheng Zhang , Da-jun Zhang
We construct multi-soliton solutions of the n-component vector nonlinear Schrdinger equation on the half-line subject to two classes of integrable boundary conditions (BCs): the homogeneous Robin BCs and the mixed Neumann/Dirichlet BCs. The construction is based on the so-called dressing the boundary, which generates soliton solutions by preserving the integrable BCs at each step of the Darboux-dressing process. Under the Robin BCs, examples, including boundary-bound solitons, are explicitly derived; under the mixed Neumann/Dirichlet BCs, the boundary can act as a polarizer that tunes different components of the vector solitons. Connection of our construction to the inverse scattering transform is also provided.
中文翻译:
矢量NLS孤子与边界相互作用
我们在半线上构造两类可积边界条件(BC)的n分量矢量非线性Schrdinger方程的多孤子解:齐次Robin BC和混合Neumann / Dirichlet BC。该构造基于所谓的修整边界,该边界通过在Darboux修整过程的每个步骤中保留可积分BC来生成孤子解。在Robin BCs下,明确推导了包括边界绑定孤子在内的示例。在Neumann / Dirichlet混合BC的作用下,边界可以充当偏振器,以调节矢量孤子的不同分量。还提供了我们的构造与逆散射变换的连接。