Solving the AKNS Hierarchy by Its Bilinear Form: Generalized Double Wronskian Solutions

通过 Wronskian 技术，一个简单、直接的证明被介绍在双线性的形式的 AKNS 层次概括了两倍 Wronskian 答案。而且由使用一个统一方法，在为它的两倍 Wronskian 形式的 soliton 答案，合理答案， Matveev 答案和 complexitons 被构造。

A Hierarchy of Integrable Lattice Soliton Equations and New Integrable Symplectic Map

开始从一分离光谱问题， integrable latticesoliton 方程的一个层次被导出。层次是，这被显示出完全在 theLiouville 感觉的 integrable 并且拥有分离 bi-Hamiltonian 结构。一张新 integrable symplectic 地图 andfinite 维的 integrable 系统被 nonlinearization 方法给。二进制 Bargmannconstraint 为产生 integrable 格子方程产生 Baecklund 转变。最后，层次的能量守恒定律被介绍。

High-Order Binary Symmetry Constraints of a Liouville Integrable Hierarchy and Its Integrable Couplings

<Abstract>A 3×3 matrix spectral problem and a Liouville integrable hierarchy are constructed by designing a new subalgebra of loop algebra _2.Furthermore,high-order binary symmetry constraints of the corresponding hierarchy are obtained by using the binary nonlinearization method.Finally,according to another new subalgebra of loop algebra _2, its integrable couplings are established.

N-Soliton Solutions of(2+1)-Dimensional Non-isospectral AKNS System

The bilinear form of the(2+1)-dimensional non-isospectral AKNS system is derived.Its N-soliton solutionsare obtained by using the Hirota method.As a reduction,a(2+1)-dimensional non-isospectral Schrdinger equation andits N-soliton solutions are constructed.