Analytical Solutions to Generalized Nonlinear Schrödinger Equation by Adomian Decomposition Technique

Analytical Soliton Solutions Modeling of Nonlinear Schrödinger Equation with the Dual Power Law Nonlinearity  

Introduction In this study, we use a newly proposed method based on the software structure of the maple, called the Khaters method, and will be introducing exponential, hyperbolic, and trigonometric solutions for one of the Schrödinger equations, called the nonlinear Schrödinger equation with the dual power law nonlinearity. Given the widespread use of the Schrödinger equation in physics and e...

Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation.

A discrete Adomian decomposition method for discrete nonlinear Schrödinger equations

We present a new discrete Adomian decomposition method to approximate the theoretical solution of discrete nonlinear Schrödinger equations. The method is examined for plane waves and for single soliton waves in case of continuous, semi– discrete and fully discrete Schrödinger equations. Several illustrative examples and Mathematica program codes are presented.

Solving the oscillating electric dipole equation by Adomian decomposition technique

For modeling the electric organ discharge of Malapterurus electricus catfish we have set up the electromechanical scheme of the catfish as an electric dipole the charges of which are linked by a spring of stiffness k. We call this particular system of charges an oscillating electric dipole. Taking into account the main forces applied to this dipole and applying the Newton’s second law of motion...

Analytical Solutions to a Generalized Growth Equation

occur in the analysis of biological networks. They also include as special cases the known growth laws and probability functions, famous differential equations like those of Bessel, Chebyshev, and Laguerre, and solutions to important physical problems. These systems have no known analytical solution. However, an important subclass comprising many of the special cases mentioned above is solved. ...