2022
DOI: 10.1177/14613484221135478
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Exact solutions for the conformable fractional coupled nonlinear Schrödinger equations with variable coefficients

Abstract: In this work, the general algebraic method is proposed for finding some solutions of a conformable fractional coupled nonlinear Schrödinger equation with variable coefficients arising in inhomogeneous fibers with two orthogonal polarization states. With the aid of symbolic computations, many types of new soliton pulse and periodic pulse solutions including complex doubly periodic solutions, solitary wave solutions, and trigonometric function solutions are obtained. Some 3D and 2D numerical simulations about th… Show more

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Cited by 8 publications
(4 citation statements)
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“…Remark. Solutions u i (i = 1, 7, 9, 10,11,12,13,14,15,17,19,29,30,31) are degenerated to solitary solutions when the modulus m → 1 , and solutions u i (i = 1,4,5,8,11,12,15,17,19,21,23,27,28,31) are degenerated to triangular functions solutions when the modulus m → 0 .…”
Section: Exact Solutions To the Fractional (3 + 1)-dimensional Kp Equ...mentioning
confidence: 99%
See 1 more Smart Citation
“…Remark. Solutions u i (i = 1, 7, 9, 10,11,12,13,14,15,17,19,29,30,31) are degenerated to solitary solutions when the modulus m → 1 , and solutions u i (i = 1,4,5,8,11,12,15,17,19,21,23,27,28,31) are degenerated to triangular functions solutions when the modulus m → 0 .…”
Section: Exact Solutions To the Fractional (3 + 1)-dimensional Kp Equ...mentioning
confidence: 99%
“…[8][9][10][11]. To date, many powerful methods have been proposed for this subject, such as the Bäcklund transformation method [12], Darboux transformation [13], Hirota bilinear method [14], improved F-expansion method [15], sine-Gordon method [16], projective Riccati equations method [17], G'/G-expansion method [18], (G'/G,1/G)-expansion method [19], improved (m + G'/G)-expansion method [20], improved G'/G 2 -expansion method [21], the first integral method [22], Generalized Exp-Function Method [23], Exp(−ϕ(ξ))-Expansion Method [24], and Lie symmetry method, which are connected to the wave transformations of equations that do not change the set of solutions [25], among others [26][27][28][29][30][31][32][33][34][35][36].…”
Section: Introductionmentioning
confidence: 99%
“…The improved F-expansion method, 21 projective Riccati equations method, 22 Jacobi elliptic function expansion method, 23 Gʹ/G-expansion method, 24 (d + Gʹ/G)-expansion method, 25 (Gʹ/G, 1/G)-expansion method, 26 sine Gordon method, 27 Lie symmetry method, 28 new Kudryashov's method, 29 auxiliary equation method, 30 exponential rational function method, 31 etc. [32][33][34][35][36][37][38][39][40][41][42] can be used to find doubly periodic solutions, solitary wave solutions, and trigonometric function solutions of these models. More research on the exact solutions, approximate solutions, and dynamic analysis of fractional systems can be found in Refs.…”
Section: Introductionmentioning
confidence: 99%
“…Fractional calculus has triggered much interest in both physics and mathematics [1,2]. Traditional differential equations cannot accurately represent many physical problems, and the fractional partner can provide deeper insight into these complex physical phenomena with ease.…”
Section: Introductionmentioning
confidence: 99%