Degenerate solutions for the spatial discrete Hirota equation

• DOI: 10.1007/s11071-020-05973-0
• Publication Date: 2020-10-07T00:02:37Z
• Authors: Meng Li; Maohua Li; Jingsong He
• Keywords: Breather

In this paper, some degenerate solutions of the spatial discrete Hirota equation are constructed via the degenerate idea of positon solution. Under the zero seed solution, the n-positon is obtained by N-fold degenerate Darboux transformation (DT). The degenerate DT is taking the degenerate limit $$\lambda _{j}\rightarrow \lambda _{1}$$ for the eigenvalues $$\lambda _{j}(j=1,2, 3, \ldots , N)$$ of N-fold DT and then performing the high-order Taylor expansion near $$\lambda _{1}$$ . Considering the universal Darboux transformation, breather is obtained from the nonzero seed. Then, a new type of breather solution can be produced by using the same degenerated method and higher-order Taylor expansion for eigenvalues in determinant expression of breather solution. The explicit determinants of breather-positon solution and positon solution are constructed, respectively, and the complicated and significant dynamics of low-order solution are also revealed.