Higher Dimensional Chen-Lee-Liu Equation and Asymmetric Peakon Soliton

Abstract

Integrable systems play a crucial role in physics and mathematics. In particular, the traditional (1 + 1)-dimensional and (2 + 1)-dimensional integrable systems have received significant attention due to the rarity of integrable systems in higher dimensions. Recent studies have shown that abundant higher dimensional integrable systems can be constructed from (1 + 1)-dimensional integrable systems by using a deformation algorithm. In this manuscript, a new (2 + 1)-dimensional Chen-Lee-Liu (C-L-L) equation is established using the deformation algorithm from the (1+1)-dimensional C-L-L equation. The new system is integrable with its Lax pair obtained by applying the deformation algorithm to that of the (1 + 1)-dimension. It is challenging to obtain the exact solutions for the new integrable system because the new system combines both the original C-L-L equation and its reciprocal transformation. The traveling wave solutions are derived in implicit function expression and some asymmetry peakon solutions are found.