• Modulational instability and dynamics of discrete rational soliton and mixed interaction solutions for a higher-order nonlinear self-dual network equation

• # Fulltext

https://www.ias.ac.in/article/fulltext/pram/095/0045

• # Keywords

Higher-order nonlinear self-dual network equation; discrete generalised $(m, N − m)$-fold Darboux transformation; rational soliton solutions; mixed interaction solutions; numerical simulation.

• # Abstract

In this paper, the higher-order nonlinear self-dual network equation is investigated. Firstly, an integrable lattice hierarchy associated with this equation is constructed from a discrete matrix spectral problem without the denominator. Secondly, the condition of modulational instability for this equation is given. Thirdly, the infinitely many conservation laws are constructed on the basis of its new Lax representation. Finally, the discrete generalised $(m, N − m)$-fold Darboux transformation (DT) with non-zero constant as seed solution is used to derive new rational soliton (RS) and mixed interaction solutions. As an application, RS solutions can be obtained by the discrete generalised $(1, N −1)$-fold DT (i.e., generalised $(m, N −m)$-fold DT with $m = 1$), and mixed interaction solutions of the usual sech-type soliton (US) and RS can be derived by the discrete generalised $(2, N −2)$-fold DT (i.e., generalised $(m, N − m)$-fold DT with $m = 2$). We also perform the numerical simulations for such soliton solutions to explore their dynamical behaviours. Results given in this paper may have some prospective applications for understanding the propagation of electrical signals.

• # Author Affiliations

1. School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China

• # Pramana – Journal of Physics

Volume 95, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019