Degenerate Solutions of the Nonlinear Self-Dual Network Equation |
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Authors: | Ying-Yang Qiu Jing-Song He Mao-Hua Li |
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Affiliation: | Department of Mathematics, Ningbo University, Ningbo 315211, China |
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Abstract: | The N-fold Darboux transformation (DT) Tn[N] of the nonlinear self-dual network equation is given 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 given 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 given analytically, which provide excellent fit of exact trajectories. These orbits have a time-dependent "phase shift", namely ln(t2). |
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Keywords: | nonlinear self-dual network equation Darboux transformation soliton degenerate solution |
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