论文标题
具有非零边界条件的一般耦合的海洛塔系统的逆散射变换
Inverse scattering transform of the general coupled Hirota system with nonzero boundary conditions
论文作者
论文摘要
通过报告逆散射变换的严格理论，解决了无数边界条件的一般耦合的海洛塔系统的初始值问题。借助合适的统一变量，分析了逆问题和直接问题，这使我们能够在复杂的$ z $平面上开发反向散射变换。首先，详细讨论了散射本征函数和散射数据，离散频谱，对称性和渐近性的特性的分析性。此外，逆问题被视为特征函数的Riemann-Hilbert问题，并提出了潜力的重建公式，以本征函数和散射数据的形式。最后，在$ 2 \ times2 $自我关注的情况下以图形方式讨论了这些获得的孤子解决方案的主要特征。这个解决方案家族包含新颖的Akhmedieev呼吸器和Kuznetsov-Ma Soliton。这些结果在理解和丰富非线性和复杂系统（尤其是Bose-Einstein凝结物）中引起的呼吸波现象非常重要。
The initial value problem for the general coupled Hirota system with nonzero boundary conditions at infinity is solved by reporting a rigorous theory of the inverse scattering transform. With the help of a suitable uniformization variable, both the inverse and the direct problems are analyzed which allows us to develop the inverse scattering transform on the complex $z$-plane. Firstly, analyticity of the scattering eigenfunctions and scattering data, properties of the discrete spectrum, symmetries, and asymptotics are discussed in detail. Moreover, the inverse problem is posed as a Riemann-Hilbert problem for the eigenfunctions, and the reconstruction formula of the potential in terms of eigenfunctions and scattering data is presented. Finally, the main characteristics of these obtained soliton solutions are graphically discussed in the $2\times2$ self-focusing case. This family of solutions contains novel Akhmediev breather and Kuznetsov-Ma soliton. These results would be of much importance in understanding and enriching breather wave phenomena arising in nonlinear and complex systems, especially in Bose-Einstein condensates.
