This article investigates a nonlinear fifth-order partial differential equation (PDE) in two-
mode waves. The equation generalizes two-mode Sawada-Kotera (tmSK), two-mode Lax …

We analyze N-soliton solutions and explore the Hirota N-soliton conditions for scalar (1+ 1)-
dimensional equations, within the Hirota bilinear formulation. An algorithm to verify the …

This research aims to investigate a generalized fifth-order nonlinear partial differential
equation for the Sawada-Kotera (SK), Lax, and Caudrey-Dodd-Gibbon (CDG) equations to …

The Handbook of Nonlinear Partial Differential Equations is the latest in a series of
acclaimed handbooks by these authors and presents exact solutions of more than 1600 …

Bilinearization of nonlinear partial differential equations (PDEs) is essential in the Hirota
method, which is a widely used and robust mathematical tool for finding soliton solutions of …

Two straightforward methods for finding solitary-wave and soliton solutions are presented
and applied to a variety of nonlinear partial differential equations. The first method is a …

In this work we use the Hirota's direct method combined with the simplified version of this
method to determine the N-soliton solutions, N= 1, 2, 3, 4, 5 for the Kadomtsev–Petviashvili …

A new algorithm for the symbolic computation of polynomial conserved densities for systems
of nonlinear evolution equations is presented. The algorithm is implemented inMathematica …

With the inhomogeneities of media taken into account, under investigation is hereby a
generalized variable‐coefficient forced Korteweg‐de Vries (vc‐fKdV) equation, which …

A selective classified bibliography of symbolic computation in some areas of chemistry is
provided together with some examples of computer algebra algorithms and techniques to …