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In this paper, the generalized (3+1)-dimensional nonlinear wave equation in fluid with gas bubbles is studied in soliton theory and produced by taking the Hirota bilinear operators. The first- to third rogue wave solutions through numerous rogue wave strategy by Maple typical estimations are recovered. The made conditions for the analyticity and positively of the gotten arrangements can be effectively accomplished by utilizing the specific determinations of the included values. The most merits of this plot are to recoup the Hirota bilinear models and their generalized equivalences. Also, the rational tan (Π (ξ)) technique on the generalized nonlinear wave equation is examined. The perturbed solution of the generalized nonlinear wave equation through the way of Modulational stability is studied. Finally, the graphical reenactments of the precise arrangements are portrayed. By selecting suitable values for the parameters involved in the solutions, 3D graphs, 2D contour graphs and line graphs are presented to provide graphical demonstration of the results. The reported results will be helpful to design new and better optical devices. The findings of this work may also help in problems arising in ocean engineering. [ABSTRACT FROM AUTHOR]

In this paper, the generalized (3+1)-dimensional nonlinear wave equation in fluid with gas bubbles is studied in soliton theory and produced by taking the Hirota bilinear operators. The first- to third rogue wave solutions through numerous rogue wave strategy by Maple typical estimations are recovered. The made conditions for the analyticity and positively of the gotten arrangements can be effectively accomplished by utilizing the specific determinations of the included values. The most merits of this plot are to recoup the Hirota bilinear models and their generalized equivalences. Also, the rational tan(Π(ξ)) technique on the generalized nonlinear wave equation is examined. The perturbed solution of the generalized nonlinear wave equation through the way of Modulational stability is studied. Finally, the graphical reenactments of the precise arrangements are portrayed. By selecting suitable values for the parameters involved in the solutions, 3D graphs, 2D contour graphs and line graphs are presented to provide graphical demonstration of the results. The reported results will be helpful to design new and better optical devices. The findings of this work may also help in problems arising in ocean engineering.

Under investigation in this paper is the (2 + 1) -dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equation. Based on bilinear method, the multiple rogue wave solutions and the novel multiple soliton solutions are constructed by giving some specific activation functions in the considered model. By means of symbolic computation, these analytical solutions and corresponding rogue waves are obtained, via Maple 18. By utilizing improved tan (Φ (ρ) ∕ 2) -expansion technique the series of novel exact solutions in terms of rational, periodic and hyperbolic functions for the fractional cases are derived. Also, the semi-inverse variational principle is offered to get the solitary solutions. We construct the exact lump and rogue wave solutions, by solving the under-determined nonlinear system of algebraic equations for the specified parameters. Via various three-dimensional plots, curve plots, density plots and contour plots, dynamical characteristics of these waves are represented. [ABSTRACT FROM AUTHOR]