New Soliton and Periodic Wave Solutions to the Fractional DGH Equation Describing Water Waves in a Shallow Regime

Simulation of a Combined (2+1)-Dimensional Potential Kadomtsev–Petviashvili Equation via Two Different Methods

“…The examination of solutions of these equations has become crucial across various fields of science and technology, including control theory, fiber optics, solid-state mechanics, transport infrastructure, atomic engineering, fluid dynamics, and various other research fields. Numerous successful approaches have been devised for investigating dynamic structures, such as lump solutions [1,2], the matrix eigenvalue problem [3], auto-Backlund transformations [4], the auxiliary equation method [5], the generalized Riccati equation mapping technique [6], the addendum to the Kudryashov technique [7], the unified method [8], the modified extended tanh-function approach [9], the Hirota bilinear technique [10], the Lie symmetry approach [11], the improved Bernoulli sub-equation function procedure [12], the modified (G ′ /G)-expansion method [13], the bilinear method [14], an extended (G ′ /G)-expansion method [15], the tanh-coth method [16,17], and so on.…”

New analytical solutions and integrability for the (2 + 1)-dimensional variable coefficients generalized Nizhnik-Novikov-Veselov system arising in the study of fluid dynamics via auto-Backlund transformation approach

“…-expansion approach and the sine-Gordon expansion method in [19]; the analytic solutions to a generalized super-NLS-mKdV equation are determined by employing the Darboux transformation technique in [20]; the solution families in the form of Jacobi elliptic function to the resonant NLS equation have been derived via a new Ф 6 -model expansion approach in [21]; modified Pfaffian technique is utilized to derive the hybrid wave solutions of shallow water wave equation in (2 + 1)-dimensions in [22] and to find the nonlinear wave solutions of generalized (3 + 1)dimensional Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in [23]; modified tanh-expansion approach is used to obtain the optical solutions of Fokas-Lenells equation in [24]; Hirota bilinear method has been utilized to derive the breather, soliton, and rogue wave solutions of cylindrical Kadomtsev-Petviashvili equation in [25]; auxiliary equation approach is utilized to derive the periodic wave solutions of fractional Dullin-Gottwald-Holm equation in [26]; simplified Hirota method has been utilized to find the bright soliton solutions of Kadomtsev-Petviashvili-Benjamin-Bona-Mahony equations in [27] and to derive the kink-type multi-soliton solutions of the Mikhailov-Novikov-Wang (MNW) equation in [28]; Painlevé analysis method is utilized to examine the integrability of MNW equation in [29]; Painlevé analysis approach along with auto-Bäcklund transformation approach is employed to find the integrability and numerous analytical solutions of variable coefficients generalized (2 + 1)-dimensional Burgers system in [30], generalized KdV6 equation with variable coefficients in [31] and modified variable coefficients KdV equation in [32].…”