Analysis on construction and evolution dynamics for multi-lump solutions of the dispersive long wave equations

This paper investigates the dispersive long wave equations that can be used to describe wide channels or open oceans with finite depth. By utilizing the Binary Darboux transform and the generalized Schur polynomial, the 2N-lump solutions are constructed. Subsequently, different dynamic behaviors are analyzed, such as (1) The 2N lumps can be divided into N groups, and each group is composed of a principal peak and an adjoint peak; (2) The deflection of peak trajectories in the rs-plane by \(90^\circ \) ${90}^{\circ }$ after collision, which can be explained by correlating the peak positions with the roots of the heat polynomials; (3) The peak locations are separated in the scales as when \(\left| t\right| \rightarrow \infty \) $\left|t\right|\to \infty$ ; (4) For the peak heights of the principal peaks, we can find that their heights are time-dependent and will tend to the same constant value.