Modulational instability and sister chirped femtosecond modulated waves in a nonlinear Schrödinger equation with self-steepening and self-frequency shift

Embed-Solitons in the Context of Functions of Symmetric Hyperbolic Fibonacci

“…The arbitrary function f (x, z, t) contained in the former resolutions indicates that the natural quantities u, v, and w have loaded constructions. For instance, rich localized excitements, e.g., lumps, instantons, dromions, ghostons, peakons, breathers, compactons, fractal and chaotic patterns, ring solitons, and their interactions [6][7][8][9], may be obtained by the potential U ≡ u 15, x , which is ignored in this paper because comparable situations were reported in the literature [6][7][8][9]. The present paper discusses some novel localized excitations, including the taper-like solitons, rectangle-soliton, plateau-type ring solitons, embed-solitons, as well as their interactions which has many applications in applied physics with the light of U ≡ u 15,x , namely…”

“…However, the literature on solitary waves of the non-propagating type in higher dimensions, particularly in systems with the (2+1)-dimensional non-linearity, is deficient despite several theoretical and practical works [6,7]. Recently, there has been a formula that works for everyone [7]. u= 2(a 2 a 1 −a 3 a 0 )q y p x (a 0 +a 1 p+a 2 q+a 3 pq) 2 (1)…”

“…Equation ( 1) fits the appropriate potential or physical fields for an enormous kind of (2+1)-dimensional, naturally stimulating nonlinear equations and systems. Examples include the dispersive long wave (DLW) systems, Davey-Stewartson (DS), Broer-Kaup-Kupershimidt (BKK) system, asymmetric DS, Nizhnik-Novikov-Veselov (NVV), asymmetric NNV system, generalized NNV equation, Maccari system, long wave-short wave interaction model, general (N+M)-component AKNS system, (2+1)-dimensional Ablowitz-Kaup-Newell-Segur (AKNS) system, (2+1)-dimensional KdV equation, as well as (2+1)dimensional sine-Gordon Equation [6][7][8], depending on the technique of multilinear variable separation. In (1), the function p ≡ p(x, t) represents the {x, t} arbitrary function.…”

Novel constructed dark, bright, and rogue waves of three models of the well-known nonlinear Schrödinger equation

“…As a result, tackling nonlinear issues is critical in nonlinear sciences [4,5]. Numerous successful techniques for deriving explicit solutions to NPDEs have been proposed, including Khater method, modified Khater method, generalized Khater method, simplest equation method, (G ′ /G)-expansion method, Tanh method, sech-tanh method, Riccati expansion method and so on [6,7,8]. Exact solutions to nonlinear evolution equations are critical in studying soliton theory, and explicit formulations for NPDEs [9,10].…”