Optical solitons in medium with parabolic law nonlinearity and higher order dispersion

On some new analytical solutions for new coupled Konno–Oono equation by the external trial equation method

“…The graphical representations of these solutions are shown in figures 1-10 respectively.4.1. Discussion and remarksBy help of ETEM, we obtain solutions including exponential, hyperbolic, trigonometric and rational function forms of the new CKO equation, whereas in[5], Koçak et al acquired the traveling wave solutions including equations(25)(26)(27)(28)(29)(30)(31)(32) in which obtained by using MEFM. Meanwhile, in this paper are new hyperbolic and complex function solutions in which agree with results of[5].…”

“…Authors of [5] obtained trawling wave solution for coupled Konno-Oono (CKO) equation using the modified exponential function method. A special case of system (1.1) to be considered transformed into new Konno-Oono equation system which is a coupled integrable dispersionless equations given as form of: )-expansion method [13][14][15], the G G ¢ -expansion method [16,17], the generalized G G ¢ -expansion method [18], the Bernoulli sub-equation function method [19][20][21][22], the sine-Gordon expansion method [23][24][25], the Ricatti equation expansion [26], the formal linearization method [27], the Lie symmetry [28][29][30], the Bäcklund transformations [31][32][33], the Darboux transformation [34], the Fokas method [35][36][37], the Hirota bilinear method [38][39][40][41]43], and so on.…”

Solitons in optical metamaterials with anti-cubic law of nonlinearity by ETEM and IGEM

“…This paper will quell the thirst partially. In the past, solitons in optical metamaterials have been studied with various forms of non-Kerr laws of nonlinearity where several integration schemes have been implemented [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Interested reader also read herein references [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”

“…(1), the unknown or dependent variable q(x, t) represents the wave profile, while x and t are the spatial and temporal variables respectively. The first and second terms are the linear temporal evolution term and group velocity dispersion (GVD), while third term introduces the anti-cubic nonlinear term, fourth and fifth terms account for the parabolic law nonlinearity, and sixth, seventh and eighth terms represent the IMD, SS and *Correspondence: manafianheris@tabrizu.ac.ir 2 Department of Mathematics, Ilkhchi Branch, Islamic Azad University, Ilkhchi, Iran Full list of author information is available at the end of the article ND respectively. Finally, the last three terms with θ k for k = 1, 2, 3 appear in the context of metamaterials [3,4].…”

“…In the presence of parabolic law nonlinearity, with an additional anticubic nonlinear term and perturbation terms that include inter-modal dispersion (IMD), self-steepening (SS) as well as nonlinear dispersion (ND), the governing equation reads [1,2] iq t + aq xx + b 1 …”