Exact solutions of the nonlocal Sawada–Kotera equation in the Alice–Bob system

Abstract

To find the group invariant solution, a new shifted parity and delayed time reversal symmetries are used in order to construct Alice–Bob systems. With the help of simple assumptions and of the [Formula: see text] symmetry, the intrinsic two-place model of the Sawada–Kotera (SK) system is elucidated. A new form of the [Formula: see text]-soliton solution for the nonlocal SK equation is obtained, and dynamic properties of the [Formula: see text]-soliton solutions with different values are discussed, respectively. In addition, the breather solution for the AB–SK system is also explicitly identified.