N-soliton solution and its Wronskian form of a -dimensional nonlinear evolution equation

New (3+1)-dimensional nonlinear evolution equation: multiple soliton solutions

“…Many powerful methods were developed and used. The algebraic-geometric method [1][2][3][4][5], the inverse scattering method, the Bäcklund transformation method, the Darboux transformation method, the Hirota bilinear method [6][7][8][9][10][11][12][13][14], and others were thoroughly used to derive the multiple-soliton solutions of these equations. The Hirota's bilinear method and the simplified form of this method [10] possess significant features that make it practical for the determination of multiple soliton solutions [6][7][8][9][10][11][12][13][14] for a wide variety of nonlinear evolution equations.…”

“…was studied in [1][2][3][4][5], and in some of the references therein, to establish N-soliton solutions in order to confirm its integrability. The inverse operator ∂ −1 is defined by…”

“…In [3], the perturbation technique and the Wronskian determinant of solutions were used to determine the N-soliton solutions for the reduced equation. In [4,5], multiple soliton solutions and multiple singular soliton solutions were obtained using the simplified Hirota's method.…”

“…In [4,5], multiple soliton solutions and multiple singular soliton solutions were obtained using the simplified Hirota's method. In the present work the (3+1)-dimensional model (1) presented in [1][2][3][4][5] is extended to a new form defined by…”

Soliton Solutions, Bäcklund Transformation and Wronskian Solutions for the (2+1)-Dimensional Variable-Coefficient Konopelchenko–Dubrovsky Equations in Fluid Mechanics

“…Methods applied to constructing the analytic solutions of the NLPDEs have been proposed, such as the Hirota bilinear method [9 -14], Bäcklund transformation (BT) [9,15], Wronskian technique [16,17], Painlevé analysis [18,19], and Darboux transformation [20 -26]. The bilinear method can transform some NLPDEs into bilinear equations, e.g., the Korteweg-de Vries (KdV) [10], Gardner [27 -32], Kadomtsev-Petviashvili (KP) [33 -36] and modified KP (mKP) [37,38] equations.The Bäcklund transformation can connect several analytic solutions, and the auto-Bäcklund transformation several analytic solutions for the same equation [9,15].…”