Degenerate Solutions of the Nonlinear Self-Dual Network Equation

• 来源期刊: 理论物理通讯（英文版）
• 年，卷（期）: 2019,（1）
• 页码范围: 1-8
• 页数: 8页
• 语种: 英文
• DOI: 10.1088/0253-6102/71/1/1

摘要

The N-fold Darboux transformation (DT) Tn[N] of the nonlinear self-dual network equation is giyen in terms of the determinant representation.The elements in determinants are composed of the eigenvalues λj (j =1,2...,N) and the corresponding eigenfunctions of the associated Lax equation.Using this representation,the N-soliton solutions of the nonlinear self-dual network equation are giyen from the zero "seed" solution by the N-fold DT.A general form of the N-degenerate soliton is constructed from the determinants of N-soliton by a special limit λj → λ1 and by using the higher-order Taylor expansion.For 2-degenerate and 3-degenerate solitons,approximate orbits are giyen analytically,which provide excellent fit of exact trajectories.These orbits have a time-dependent "phase shift",namely ln(t2).