Algebro-Geometric Quasi-Periodic Solutions to the Bogoyavlensky Lattice 2(3) Equations

Localized wave solutions to the vector nonlinear Schrödinger equation with nonzero backgrounds

“…Studies of the n-component NLS equation have been done by many researchers, for examples, parity-time-symmetric rational vector RWs [29], bright solitons, energy-sharing collisions and positons with nonlocal M-component NLS equations [30], higher order vector Peregrine solitons and asymptotic estimates [31], and N-soliton solutions to the Cauchy problem of the n-component nonlinear Schrödinger equations [32]. Nowadays, researchers have developed a series of systematic methods to study nonlinear integrable systems such as Riemann-Hilbert approach [32][33][34][35], algebro-geometric method [36][37][38], nonlinear steepest decent method [39][40][41][42], and Dbar-steepest descent method [43][44][45]. In this paper, we will investigate the localized wave solutions of the vector NLS equation (1) through the generalized DT, which is a very effective tool for solving soliton equations.…”

“…Nowadays, researchers have developed a series of systematic methods to study nonlinear integrable systems such as Riemann–Hilbert approach [32–35], algebro‐geometric method [36–38], nonlinear steepest decent method [39–42], and Dbar‐steepest descent method [43–45]. In this paper, we will investigate the localized wave solutions of the vector NLS equation () through the generalized DT, which is a very effective tool for solving soliton equations.…”