Higher-order rogue waves and dispersive solitons of a novel P-type (3+1)-D evolution equation in soliton theory and nonlinear waves

In soliton theory and nonlinear waves, this research proposes a new Painleve integrable generalized (3+1)-D evolution equation. It demonstrates the Painleve test that claims the integrability of the proposed equation and employs Cole-Hopf transformations to generate the trilinear equation in an auxiliary function that governs the higher-order rogue wave and dispersive-soliton solutions via the symbolic computation approach and dispersive-soliton assumption, respectively. Center-controlled parameters in rogue waves show the different dynamical structures with several other parameters. We obtain solutions for rogue waves up to third-order using direct symbolic analysis with appropriate center parameters and other parameters using a generalized procedure for rogue waves. We assume the dispersive-soliton solution, inspired by Hirota's direct techniques to create dispersive-soliton solutions up to the third order. By applying the symbolic software Mathematica, we demonstrate the dynamical structures for rogue waves with diverse center parameters and dispersive solitons using dispersion relation to showcase the interaction behavior of the solitons. Dispersive solitons and rogue waves are fascinating phenomena that appear in diverse areas of physics, such as optical fibers, nonlinear waves, dusty plasma physics, nonlinear dynamics, and other engineering and sciences.