NEW (3+1)-DIMENSIONAL INTEGRABLE GENERALIZED KDV EQUATION: PAINLEVÉ PROPERTY, MULTIPLE SOLITON/SHOCK SOLUTIONS, AND A CLASS OF LUMP SOLUTIONS

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 Painlevé 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.