The N-loop soliton solutions for(2+1)-dimensional Vakhnenko equation

New various multisoliton kink‐type solutions of the (1 + 1)‐dimensional Mikhailov–Novikov–Wang equation

“…Over the past few years, many methods are being developed to expose new traveling solitary wave solutions for the nonlinear partial differential equation (PDE) representing the different areas of science and engineering. [1][2][3][4] Some of the analytical methods such as extended (G ′ /G)-expansion method, Darboux transformation, Pfaffian technique, sech-tanh method, sine-cosine method, Painlevé analysis, 5 Hirota bilinear method, [6][7][8][9][10][11][12][13][14][15] extended generalized Darboux transformation method, 16,17 Bäcklund transformation, and simplified Hirota's method [18][19][20][21][22][23][24] are used to solve different models involving nonlinear PDE. There is no specified method to solve all types nonlinear PDE.…”

“…Bilinear method is the method which is used to obtain analytical soliton solutions. [6][7][8][9][10][11][12][13][14][15] The Hirota bilinear method is applicable to those equations that take a bilinear form. The bilinear form of these nonlinear equation is highly nontrivial.…”

New Interaction Solutions for a (2 + 1)-Dimensional Vakhnenko Equation

“…where x 0 and y 0 are two constants and T 1 , T 2 , and X are three independent variables. Li et al [25] introduced a new function W defined by…”

“…is an implicit solution of equation (1). Some 1-loop, 2-loop, and 3-loop soliton solutions were presented applying the improved Hirota method, and the traveling and interaction processes for the N-loop soliton solutions are explored in [25]. In this paper, we investigate interaction solutions of equation 1via Hirota's transformation [26] and three-wave methods [27][28][29][30].…”

Analytic rogue wave solutions for a generalized fourth‐order Boussinesq equation in fluid mechanics

“…Many methods are used to obtain the soliton solutions for nonlinear evolution equations (NLEEs), such as G ′ / G ‐expansion method, direct method, Bäcklund transformation method, auxiliary equation method, Riccati mapping method, and Hirota bilinear transformation method . The Hirota bilinear transformation method is a classical symbolic scheme to seek for the soliton and multiple soliton solutions.…”