Bright and dark solitons of the generalized nonlinear Schrödinger’s equation

Exact solution of the Biswas-Milovic equation by Adomian decomposition method

“…Considering the complex plane C as a two-dimensional linear space R 2 , the function F (|q| 2 )q is k times continuously differentiable, so [1] F (|q|…”

“…The dynamics of the propagation of solitons is studied by the aid of nonlinear Schrodinger's equation. An improved model to describe this dynamics is Biswas-Milovic model first appeared in 2010 [1] with generalization parameter, which dictate the factor of departure from perfection. Thus Biswas-Milovic equation is of special interest in the fiber optics community.…”

Topological and Non-Topological Soliton Solutions of the Coupled Klein-Gordon-Schrodinger and the Coupled Quadratic Nonlinear Equations

“…Here, in (18) and (19) A 1 , A 2 and B are free parameters, while q is the velocity of the soliton. The unknown exponents p 1 and p 2 will be determined, The phase component of (18) and (19) is given by…”

“…Therefore solving nonlinear problems play an important role in nonlinear sciences. Many effective methods of obtaining explicit solutions of NPDEs have been presented such as the tanh-function method and its various extension [1,2], the Jacobi elliptic function expansion method [3], the homogeneous balance method [4], the F-expansion method and its extension [5], ( G ′ G )-expansion method [6], the modified simple equation method [7,8], the semi-inverse variational principle [9] the solitary wave ansatz method [10,11,12,13,14,15,16,17,18,19,20,21] and so on. It is very interesting to note that the solitary wave ansatz method has been successfully applied to many kinds of NLPDEs with constant and varying coefficients, such as, for example, the K(m, n) equation [14,21], the BBM equation [20], the B(m, n) equation [17], the nonlinear Schrodinger's equation [14,18] and many others.…”

Exact Solutions and Optical Soliton Solutions of the Nonlinear Biswas-Milovic Equation with Dual-Power Law Nonlinearity

“…The objective of this article is to use two mathematical tools, namely the first integral method and the rational (G /G) -expansion method to find the exact solutions and the solitary wave solutions of the Biswas-Milovic equation [66][67][68][69]: * corresponding author; e-mail: eme_zayed@yahoo.com i (q m ) t + a(q m ) xx + bF |q| 2 q m = 0, (1.1)…”