The partial-rogue ripple solutions of nonlocal Kadomtsev–Petviashvili equation

Abstract

The derivation of new exact solutions for integrable systems has always been an open problem in mathematical physics and engineering. In this paper, a large class of partial-rogue ripple solutions of a nonlocal Kadomtsev–Petviashvili [KP] equation are derived, which means that these ripple waves are semi-localized in time. Firstly, the Wronskian and Grammian determinant expression of the nonlocal KP equation are constructed. Then, three kinds of partial-rogue ripplon solutions of nonlocal KP equations, including (i) partial-rogue ripple soliton solutions, (ii) partial-rogue ripple lump chain solutions, and (iii) partial-rogue ripple lump solutions, are proposed. These solutions approach to the zero background plane as t→∞, which is the characteristic of partial-rogue ripple waves. These solutions are rarely reported, and their dynamics have been analytically and numerically discussed. The results of this paper are more practical and closely match the attenuated ripple waves stirred up in water waves. Additionally, the research method in this paper provides new references for existing results.