具有非零边界条件的耦合 Lakshmanan-Porsezian-Daniel 方程的逆散射变换
Inverse scattering transform for the coupled Lakshmanan-Porsezian-Daniel equation with nonzero boundary conditions
AI总结：
针对无穷远非零边界条件下的耦合 LPD 方程，本文构建逆散射变换，利用 Jost 本征函数、对称性和 Riemann-Hilbert 问题获得并分析新的精确孤子解。
摘要：
本文通过构建合适的逆散射变换，解决了在无穷远处考虑非零边界条件时求解耦合 Lakshmanan-Porsezian-Daniel 方程初值问题的挑战。文中考察了 Jost 本征函数的解析性质，并分析了散射系数的特征。该分析推导出了全面研究基本本征函数所需的附加辅助本征函数。文中讨论了两个对称条件，以研究本征函数和散射系数。这些对称性结果被用于严格定义离散谱，并确定散射数据相应的对称性。逆散射问题通过 Riemann-Hilbert 问题加以表述。随后可以由耦合 Lakshmanan-Porsezian-Daniel 方程推导精确解，并对新颖的孤子解进行了详细推导和考察。
英文摘要：
The challenge of solving the initial value problem for the coupled Lakshmanan Porsezian Daniel equation, while considering nonzero boundary conditions at infinity, is addressed through the development of a suitable inverse scattering transform. Analytical properties of the Jost eigenfunctions are examined, along with the analysis of scattering coefficient characteristics. This analysis leads to the derivation of additional auxiliary eigenfunctions necessary for the comprehensive investigation of the fundamental eigenfunctions. Two symmetry conditions are discussed to study the eigenfunctions and scattering coefficients. These symmetry results are utilized to rigorously define the discrete spectrum and ascertain the corresponding symmetries of scattering datas. The inverse scattering problem is formulated by the Riemann-Hilbert problem. Then we can derive the exact solutions by coupled Lakshmanan Porsezian Daniel equation, the novel soliton solutions are derived and examined in detail.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
