Soliton Solutions of Generalized Third-Order Nonlinear Schrödinger Equation by Using GKM

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...

Asymptotic soliton train solutions of the defocusing nonlinear Schrödinger equation.

Asymptotic behavior of initially "large and smooth" pulses is investigated at two typical stages of their evolution governed by the defocusing nonlinear Schrödinger equation. At first, wave breaking phenomenon is studied in the limit of small dispersion. A solution of the Whitham modulational equations is found for the case of dissipationless shock wave arising after the wave breaking point. Th...

Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation.

Soliton Perturbation Theory for the Generalized Fifth-Order Nonlinear Equation

The adiabatic parameter dynamics of 1-soliton solution of the generalized fifth-order nonlinear equation is obtained by virtue of the soliton perturbation theory. The adiabatic change of soliton velocity is also obtained in this paper.

Boundedness of Solutions of a Third-order Nonlinear Differential Equation

Sufficient conditions are established for the boundedness of all solutions of (1.1), and we also present some sufficient conditions, which ensure that the limits of first and second order derivatives of the solutions of (1.1) tend to zero as t→∞. Our results improve and include those results obtained by previous authors ([3], [5]).