Some novel soliton solution, breather solution and Darboux transformation for a generalized coupled Toda soliton hierarchy.

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ID: 72152
2018
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Abstract
A few of discrete integrable coupling systems(DICSs) of previous papers are linear discrete integrable couplings(LDICS). We take a special matrix Lie algebra system(non-semisimple) to construct the Lax pairs, and establish a method for deriving the nonlinear discrete integrable coupling systems(NDICS). From the Lax pairs of the generalized Toda(G-Toda) spectral problem, we can derive a novel NDICS, which is a real NDICS. For the obtained lattice integrable coupling equation, we establish a Darboux transformation (DT) with 4 × 4 Lax pairs, and apply the gauge transformation to a specific equation, then the explicit solutions of the lattice integrable coupling equation are given, which contains discrete soliton solution, breather solution and rogue wave solution. Furthermore, we can derive the discrete explicit solutions with free parameters to depict their dynamic behaviors.
Reference Key
yu2018somescientific Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Yu, Fajun;Li, Li;Feng, Shuo;
Journal Scientific reports
Year 2018
DOI
10.1038/s41598-018-33212-5
URL
Keywords
operator algebras quantum symmetry reduction unbounded operators

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