NEW (3+1)-DIMENSIONAL INTEGRABLE GENERALIZED KDV EQUATION: PAINLEVE 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 complete integrability of the suggested model by demonstrating its ability to satisfy the Painleve property. The bilinear form of the (3+1)-dimensional gKdV equation is employed 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.