Multi-soliton solutions for the three-coupled KdV equations engendered by the Neumann system

Korteweg–de Vries (KdV)-type equations describe certain nonlinear phenomena in fluids and plasmas. In this paper, three-coupled KdV equations corresponding to the Neumann system of the fourth-order eigenvalue problem is investigated. Through the dependent variable transformations, bilinear forms of such equations are obtained, from which the multi-soliton solutions are derived. Soliton propagation and interaction are analyzed: (1) Bell- and anti-bell-shaped solitons are found; (2) Among the soliton images, one depends on the sign of wave numbers k i ’s ( i =1,2,3), while the others are independent of such a sign; (3) Interaction between two solitons and among three solitons are elastic, i.e., the amplitude and velocity of each soliton remain unvaried after the interaction except for the phase shift.