New (3+1)-dimensional integrable generalized KdV equation: Painlevé property, multiple soliton/shock solutions, and a class of lump solutions

Abstract

The present work aims to examine a newly proposed (3+1)-dimensional integrable generalized Korteweg-de Vries (gKdV) equation. By employing the Weiss- Tabor-Carnevale technique in conjunction with Kruskal ansatz, we establish the com- plete integrability of the suggested model by demonstrating its ability to satisfy the Painlev´e property. The bilinear form of the (3+1)-dimensional gKdV equation is em- ployed to construct multiple soliton solutions. By manipulating the various values of the corresponding parameters, we generate a category of lump solutions that exhibit localization in all dimensions and algebraic decay.