Higher-dimensional Chen-Lee-Liu equation and asymmetric peakon soliton

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. Here we establish a new (2+1)-dimensional Chen-Lee-Liu (C-L-L) equation 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.