Abundant Lump-Type Solutions and Interaction Solutions for a Nonlinear (3+1)‎ Dimensional Model

Abstract EN

We explore dynamical features of lump solutions as diversion and propagation in the space.

Through the Hirota bilinear method and the Cole-Hopf transformation, lump-type solutions and their interaction solutions with one- or two-stripe solutions have been generated for a generalized (3+1) shallow water-like (SWL) equation, via symbolic computations associated with three different ansatzes.

The analyticity and localization of the resulting solutions in the (x,y,z, and t) space have been analyzed.

Three-dimensional plots and contour plots are made for some special cases of the solutions to illustrate physical motions and peak dynamics of lump soliton waves in higher dimensions.

The study of lump-type solutions moderates the visuality of optics media and oceanography waves.