Vector multipole and vortex solitons in two-dimensional Kerr media

Solitions in magneto–optic waveguides with anti–cubic nonlinearity

“…Therefore, it is imperative to study the governing model equation in magneto–optic waveguides and secure a soliton solution for looking into additional features such as conservation laws, numerical analysis and so on. There are a variety of mathematical approaches to study soliton dynamics across the platform and these include both analytical and numerical approaches [1] , [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] . The conserved quantities thus emerged are applicable to the study of soliton p…”

Analytical Insights into a Generalized Semidiscrete System with Time-Varying Coefficients: Derivation, Exact Solutions, and Nonlinear Soliton Dynamics

“…In 2005, Yang and Xu [49] developed a direct method for constructing integrable expanding models for semidiscrete systems. In soliton theory, there are many methods like those in [50][51][52][53][54][55][56][57][58] besides the inverse scattering method [59] for solving nonlinear differential equations. In this paper, we shall analytically derive and solve system (1) by means of the inverse scattering analysis.…”

Resonant Soliton and Soliton‐Cnoidal Wave Solutions for a (3+1)‐Dimensional Korteweg‐de Vries‐Like Equation

“…In scientific and engineering fields, nonlinear evolution equations have been studied in wide applications, such as in the nonlinear optics [1][2][3][4][5][6][7], plasma physics [8,9], fluid mechanics [10,11], textile engineering [12], and wave propagation phenomena [13][14][15][16]. Explicitly, for finding solutions, which including solitons, cnoidal waves, Painlevé waves, Airy waves, Bessel waves, etc., people often take the symmetry reduction approach with nonlocal symmetries with the aid of Darboux transformation, Bäklund transformation, and residual symmetry [17][18][19][20][21].…”