Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTwo-component nonlinear wave of the NLS equation
73
0
0.0
(
0
)
Authors
G. T. Adamashvili
Ask ChatGPT about the research
No Arabic abstract
Using the generalized perturbation reduction method the scalar nonlinear Schrodinger equation is transformed to the coupled nonlinear Schrodinger equations for auxiliary functions. A solution in the form of a two-component vector nonlinear pulse is obtained. The components of the pulse oscillate with the sum and difference of the frequencies and wave numbers. Explicit analytical expressions for the shape and parameters of the two-component nonlinear pulse are presented.
rate research
Read More
This is a continuation of Ref.[1](arXiv:nlin.PS/2001.07758v1). In the present paper, we consider the solution to the modified Benjamin-Bona-Mahony equation $u_{ t} + C u_{z} + beta u_{zzt} + a u^{2} u_{z}=0$ using the generalized perturbation reduction method. The equation is transformed to the coupled nonlinear Schrodinger equations for auxiliary functions. Explicit analytical expression for the shape and parameters of the two-component vector breather oscillating with the sum and difference of frequencies and wavenumbers are obtained.
Using the generalized perturbation reduction method the Hirota equation is transformed to the coupled nonlinear Schrodinger equations for auxiliary functions. A solution in the form of a two-component vector nonlinear pulse is obtained. The components of the pulse oscillate with the sum and difference of the frequencies and the wave numbers. Explicit analytical expressions for the shape and parameters of the two-component nonlinear pulse are presented.
In this work, we employ the generalized perturbation reduction method to find the two-component vector breather solution of the cubic Boussinesq equation $U_{tt} - C U_{zz} - D U_{zzzz}+G (U^{3})_{zz}=0$. Explicit analytical expressions for the shape and parameters of the two-component nonlinear pulse oscillating with the sum and difference of the frequencies and wave numbers are obtained.
The generalized perturbative reduction method is used to find the two-component vector breather solution of the Born-Infeld equation $ U_{tt} -C U_{zz} = - A U_{t}^{2} U_{zz} - sigma U_{z}^{ 2} U_{tt} + B U_{z} U_{t} U_{zt} $. It is shown that the solution of the two-component nonlinear wave oscillates with the sum and difference of frequencies and wave numbers.
In this paper, we study the generalized Heisenberg ferromagnet equation, namely, the M-CVI equation. This equation is integrable. The integrable motion of the space curves induced by the M-CVI equation is presented. Using this result, the Lakshmanan (geometrical) equivalence between the M-CVI equation and the two-component Camassa-Holm equation is established. Note that these equations are gauge equivalent each to other.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
