Analytic study on chirped optical solitons in nonlinear metamaterials with higher order effects

Abstract

The ultrashort pulse propagation in optical metamaterials (OMMs) modeled by a generalized nonlinear Schrödinger equation with higher order effects is studied, in the present paper. To this end, by considering a complex envelope and a specific nonlinear chirp ansatz, a wide range of exact chirped soliton solutions are derived in the presence of the pseudo-quintic nonlinearity and the self-steepening effect. Exact solutions include kink and anti-kink chirped soliton solutions that are retrieved through the use of newly well-designed methods. The complex envelopes presented herein provide new specific nonlinear shock wave structures in OMMs which are vital for numerical and experimental verifications.

The Sharma–Tasso–Olver–Burgers equation: its conservation laws and kink solitons

“…for equation (17). From equations ( 17) and (18), we will attain a nonlinear system as 3l n 2 2 0, ln 3 ln 3 ln 2 0 ,…”

“…During the past few decades, one of the major goals has been the construction of novel approaches to extract solitons for PDEs. In the last years, several well-organized methods have been proposed to derive solitons of PDEs, the hyperbolic function method [1][2][3][4], the modified Jacobi methods [5][6][7][8], the Kudryashov method [9][10][11][12][13][14], and the exponential method [15][16][17][18][19][20], are samples to point out.…”

Optical solitons to the Ginzburg–Landau equation including the parabolic nonlinearity

“…Over the last several decades, one of the most significant challenges has been the development of new methods to construct exact solutions for NLPD equations. In recent years, several new, more powerful, and effective approaches have been established to retrieve exact solutions of NLPD equations, the sine-Gordon expansion method [1][2][3][4], the (𝐺 ′ 𝐺 ⁄ )-expansion method [5][6][7][8], the Sardar sub-equation method [9][10][11][12], the Kudryashov method [13][14][15][16][17][18], and the exponential method [19][20][21][22][23][24][25], are examples to mention.…”

Optical Solitons to the Ginzburg–Landau Equation Including the Parabolic Nonlinearity

“…Over the last several decades, one of the most significant challenges has been the development of new methods to construct exact solutions for NLPD equations. In recent years, several new, more powerful, and effective approaches have been established to retrieve exact solutions of NLPD equations, the sine-Gordon expansion method [1][2][3][4], the (𝐺 ′ 𝐺 ⁄ )-expansion method [5][6][7][8], the Sardar sub-equation method [9][10][11][12], the Kudryashov method [13][14][15][16][17][18], and the exponential method [19][20][21][22][23][24][25], are examples to mention.…”