Multiple lump solutions and their interactions for an integrable nonlinear dispersionless PDE in vector fields

Abstract

In this article, lump solutions, lump with I-kink, lump with II- kink, periodic, multiwaves, rogue waves and several other interactions such as lump interaction with II-kink, interaction between lump, lump with I-kink and periodic, interaction between lump, lump with II-kink and periodic are derived for Pavlov equation by using appropriate transformations. Additionally, we also present 3-dimensional, 2-dimensional and contour graphs for our solutions.

Lump Waves in a Spatial Symmetric Nonlinear Dispersive Wave Model in (2+1)-Dimensions

“…The Hirota bilinear forms and the generalized bilinear forms are the starting points exhibiting a great convenience in determining lump waves. Interaction solutions between lump waves and other interesting waves, including homoclinic and heteroclinic solutions, can be explored for integrable and nonintegrable model equations (see, e.g., [43][44][45][46][47][48]). Connections with other solution approaches in soliton theory should deserve further investigation, which include Darboux transformations [49,50], the Wronskian technique [51], auto-Bäcklund transformations [52,53], the Riemann-Hilbert technique [54][55][56], symmetry reductions [57,58] and symmetry constraints [59].…”