A (2+1)-dimensional Kadomtsev–Petviashvili equation with competing dispersion effect: Painlevé analysis, dynamical behavior and invariant solutions

The Extended Direct Algebraic Method for Extracting Analytical Solitons Solutions to the Cubic Nonlinear Schrödinger Equation Involving Beta Derivatives in Space and Time

“…The soliton solutions derived from FNLEE have practical and commercial applications in various fields such as optical fiber technology, telecommunications, signal processing, image processing, system identification, water purification, plasma physics, medical device sterilization, chemistry, and other related domains [1,2]. Various dynamic approaches have been introduced and implemented in the literature to solve nonlinear fractional differential equations (NFDES) and obtain analytical traveling wave solutions, for example, the exp-function method [3], the Modified Exp-function method [4], the inverse scattering transformation method [5,6], the Bäcklund transformation method [7], the homogenous balance method [8,9], the Jacobi elliptic function method [10], the unified algebraic method [11], the sine-cosine method [12,13], the tanh-coth method [14,15], improved modified extended tanh-function method [16,17], the Lie symmetry analysis method [18], the extended generalized (G /G)-expansion method [19], the modified simple equation method [20], the generalized Kudryashov method [21,22], the sine-Gordon expansion method [23], the Riccati-Bernoulli equation method [24,25], the new extended direct algebraic method [26,27], and the new auxiliary equation method [28].…”

Optical soliton solutions of the coupled Radhakrishnan-Kundu-Lakshmanan equation by using the extended direct algebraic approach

“…It is necessary to solve the models under discussion precisely by using suitable methods. The study of exact solutions to nonlinear PDEs has been an active field of research which plays an important role in the study of their applications in the real world [1] , [2] , [3] , [4] . Various computational techniques have been proposed until now for obtaining the exact solutions to nonlinear equations.…”

Rogue wave solutions of (3+1)-dimensional Kadomtsev-Petviashvili equation by a direct limit method

“…where δ, μ and χ are parameters, u is a wave amplitude function of {x, y, z, t}. The (3+1)-dimensional KP equation has been extensively studied in many fields, it can be used to research hydrodynamics [30], plasma physics [31,32], the dynamical behavior of nonlinear waves [33], etc. Therefore, studying the solutions of the (3+1)-dimensional KP equation is meaningful.…”