Optical solitons with perturbed complex Ginzburg–Landau equation in kerr and cubic–quintic–septic nonlinearity

Exact solutions to the fractional complex Ginzburg-Landau equation with cubic-quintic and Kerr law nonlinearities

“…When p = 2, it leads to elliptic and soliton wave solutions. Inserting equation (9) into equation (8), combining all power coefficients of f(η) and making their results to zero, p i (t), q i (t) and b i (t) can be gotten. Through solving the auxiliary equations in equation (9), the solutions of equation (8) can be given.…”

“…First, we need to poise the highest derivative and the highest nonlinear terms in equation (8) to get the value of n. After all these, through substituting equation (10) and equation (11) into equation (8), collecting all power moduli of (μ + F(η)) and making their results to zero, the values of a i and c i can be given. Then, the bright and dark solitons solutions of equation ( 8) can be given immediately.…”

“…Before we gain the exact solutions of equation (8), we must attain the value of n by balancing the highest derivative and the highest nonlinear terms After substituting equation (13) into equation (8), gathering all power moduli of ( ) ¢ G G 2 and making them to zero, the constants λ, μ, ρ and functions h i (t), s i (t) can be obtained. In virtue of equation ( 15), the traveling wave solutions of equation ( 8) can be gotten naturally.…”

“…Similarly, the value of n and m can be gotten according to the balance of the highest derivative and the highest nonlinear terms Then, inserting equation ( 16) and equation (17) into equation (8), collecting all power coefficients of Ω(η) and making them to zero, we can gain the forms of ò i (t) and ω i (t). With the help of the solutions for the Bernoulli differential equation, the exact solutions of equation ( 8) can be given easily.…”

“…The complex Ginzburg-Landau equation is a typical model of weakly nonlinear dissipative systems and one of the most studied nonlinear equations in physics, which can be used to describe a wide variety of nonlinear phenomena, such as nonlinear photonics, dynamic phase changes, superconductivity, superfluid, fluid dynamics, plasma, Bose-Einstein condensation, liquid crystals, field theory strings and so on [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. In its most basic forms, the complex Ginzburg-Landau equation includes the cubic nonlinearity [1] and has the following form [3] (…”