Novel Multi-soliton Solutions in (2+1)-Dimensional PT-Symmetric Couplers with varying coefficients

Optik ◽  
2021 ◽  
pp. 168495
Author(s):  
Shaofu Wang
Keyword(s):  
Soliton Solutions ◽  
Varying Coefficients

Analytical Insights into a Generalized Semidiscrete System with Time-Varying Coefficients: Derivation, Exact Solutions, and Nonlinear Soliton Dynamics

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Sheng Zhang ◽  
Sen Zhao ◽  
Bo Xu
Keyword(s):  
Inverse Scattering ◽  
Soliton Solutions ◽  
Time Varying ◽  
Varying Coefficient ◽  
Varying Coefficients ◽  
Soliton Dynamics ◽  
Special Cases ◽  
Time Varying Coefficients ◽  
Matrix Spectral Problem ◽  
Propagation Velocities

In this paper, a new generalized semidiscrete integrable system with time-varying coefficients is analytically studied. Firstly, the generalized semidiscrete system is derived from a semidiscrete matrix spectral problem by embedding finite time-varying coefficient functions. Secondly, exact and explicit N-soliton solutions of the semidiscrete system are obtained by using the inverse scattering analysis. Finally, three special cases when N=1,2,3 of the obtained N-soliton solutions are simulated by selecting some appropriate coefficient functions. It is shown that the time-varying coefficient functions affect the spatiotemporal structures and the propagation velocities of the obtained semidiscrete one-soliton solutions, two-soliton solutions, and three-soliton solutions.

On the Exact Soliton Solutions of Some Nonlinear PDE by Tan-Cot Method

2018 ◽  
Vol 5 (1) ◽  
pp. 31-36
Author(s):  
Md Monirul Islam ◽  
Muztuba Ahbab ◽  
Md Robiul Islam ◽  
Md Humayun Kabir
Keyword(s):  
Solitary Wave ◽  
Acoustic Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Rectangular Channel ◽  
Soliton Solutions ◽  
Boussinesq Equations ◽  
Travelling Wave ◽  
Ion Acoustic Waves ◽  
Analytical System

For many solitary wave applications, various approximate models have been proposed. Certainly, the most famous solitary wave equations are the K-dV, BBM and Boussinesq equations. The K-dV equation was originally derived to describe shallow water waves in a rectangular channel. Surprisingly, the equation also models ion-acoustic waves and magneto-hydrodynamic waves in plasmas, waves in elastic rods, equatorial planetary waves, acoustic waves on a crystal lattice, and more. If we describe all of the above situation, we must be needed a solution function of their governing equations. The Tan-cot method is applied to obtain exact travelling wave solutions to the generalized Korteweg-de Vries (gK-dV) equation and generalized Benjamin-Bona- Mahony (BBM) equation which are important equations to evaluate wide variety of physical applications. In this paper we described the soliton behavior of gK-dV and BBM equations by analytical system especially using Tan-cot method and shown in graphically. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 5(1), Dec 2018 P 31-36

scholarly journals Dispersive MHD waves and alfvenons in charge non-neutral plasmas

2008 ◽  
Vol 15 (4) ◽  
pp. 681-693 ◽  
Author(s):  
K. Stasiewicz ◽  
J. Ekeberg
Keyword(s):  
Soliton Solutions ◽  
Theoretical Models ◽  
Mhd Waves ◽  
Space Plasmas ◽  
Charge Effects ◽  
Novel Technique ◽  
Solitary Structures ◽  
Spatial Dimensions ◽  
Electric Potentials ◽  
Linear And Nonlinear

Abstract. Dispersive properties of linear and nonlinear MHD waves, including shear, kinetic, electron inertial Alfvén, and slow and fast magnetosonic waves are analyzed using both analytical expansions and a novel technique of dispersion diagrams. The analysis is extended to explicitly include space charge effects in non-neutral plasmas. Nonlinear soliton solutions, here called alfvenons, are found to represent either convergent or divergent electric field structures with electric potentials and spatial dimensions similar to those observed by satellites in auroral regions. Similar solitary structures are postulated to be created in the solar corona, where fast alfvenons can provide acceleration of electrons to hundreds of keV during flares. Slow alfvenons driven by chromospheric convection produce positive potentials that can account for the acceleration of solar wind ions to 300–800 km/s. New results are discussed in the context of observations and other theoretical models for nonlinear Alfvén waves in space plasmas.

scholarly journals Onset of the broad-ranging general stable soliton solutions of nonlinear equations in physics and gas dynamics

2021 ◽  
Vol 20 ◽  
pp. 103762
Author(s):  
Md. Abdul Kayum ◽  
Shamim Ara ◽  
M.S. Osman ◽  
M. Ali Akbar ◽  
Khaled A. Gepreel
Keyword(s):  
Nonlinear Equations ◽  
Gas Dynamics ◽  
Soliton Solutions
Sign in / Sign up

Export Citation Format

Share Document