scholarly journals Discrete Bright-dark Soliton Interaction Dynamic Behaviors for Nonautonomous 2+1-Dimensional Soliton Equation

2021 ◽  
Author(s):  
Li Li ◽  
fajun yu
Keyword(s):  
Soliton Solution ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
The Novel ◽  
Optical Fields ◽  
Dynamic Behaviors ◽  
Spatial Part ◽  
Bright Soliton Solution ◽  
Temporal Parts ◽  
Interaction Dynamic

Abstract The non-autonomous discrete bright-dark soliton solutions(NDBDSSs) of the 2+1-dimensional Ablowitz-Ladik(AL) equation are derived. We analyze the dynamic behaviors and interactions of the obtained 2+1-dimensional NDBDSSs. In this paper, we present two kinds of different methods to control the 2+1-dimensional NDBDSSs. In first method, we can only control the wave propagations through the spatial part, since the time function has not effect in the phase part. In second method, we can control the wave propagations through both the spatial and temporal parts. The different propagation phenomena can also be produced through two kinds of managements. We obtain the novel "л"-shape non-autonomous discrete bright soliton solution(NDBSS), the novel "λ"-shape non-autonomous discrete dark soliton solution(NDDSS) and their interaction behaviors. The novel behaviors are considered analytically, which can be applied to the electrical and optical fields.

scholarly journals Soliton Solutions of a General Rosenau-Kawahara-RLW Equation

2015 ◽  
Vol 7 (2) ◽  
pp. 24 ◽  
Author(s):  
Jin-ming Zuo
Keyword(s):  
Soliton Solution ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Bright Soliton ◽  
Conserved Quantities ◽  
Rlw Equation ◽  
Bright Soliton Solution

In this paper, we consider a general Rosenau-Kawahara-RLW equation. The exact bright and dark soliton solutions for the consideredmodel are obtained by sech and tanh ansatzes methods. The mass and momentum conserved quantities are also calculated for the case of bright soliton solution.

BIFURCATIONS OF TRAVELING WAVE SOLUTIONS AND EXACT SOLUTIONS FOR THE GENERALIZED SCHRÖDINGER EQUATION

2011 ◽  
Vol 21 (09) ◽  
pp. 2623-2628
Author(s):  
JIANMING ZHANG ◽  
SHUMING LI
Keyword(s):  
Schrödinger Equation ◽  
Soliton Solution ◽  
Schrodinger Equation ◽  
Traveling Wave Solutions ◽  
Dark Soliton ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Generalized Schrödinger Equation ◽  
Bright Soliton Solution

Using the method of dynamical systems for the generalized Schrödinger equation, the bright soliton solution, dark soliton solution, uncountably infinite many periodic wave solutions and breaking bounded wave solutions are obtained. Exact explicit parametric representations of the bounded traveling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined.

scholarly journals Some analytical solutions by mapping methods for non-linear conformable time-fractional PHI-4 equation

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 1815-1822 ◽  
Author(s):  
Zeliha Korpinar
Keyword(s):  
Fractional Derivative ◽  
Periodic Solutions ◽  
Soliton Solution ◽  
Analytical Solutions ◽  
Soliton Solutions ◽  
Elliptic Functions ◽  
Dark Soliton ◽  
Optical Soliton ◽  
Conformable Fractional Derivative ◽  
Singular Soliton

In this paper, the practice of two types of mapping methods are used to solve the time fractional Phi-4 equation by means of conformable fractional derivative. The solutions are derived using Jacobi?s elliptic functions for two different value of the modulus and are obtained the some soliton solutions. The found solutions are iden?tified bright optical soliton, dark soliton, singular soliton, combo soliton solution, and periodic solutions.

Dynamics of localized waves in a (3+1)-dimensional nonlinear evolution equation

2019 ◽  
Vol 33 (09) ◽  
pp. 1950101 ◽  
Author(s):  
Yunfei Yue ◽  
Yong Chen
Keyword(s):  
Evolution Equation ◽  
Soliton Solution ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Rogue Wave ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Dark Soliton ◽  
Interaction Solutions ◽  
Localized Waves

In this paper, a (3[Formula: see text]+[Formula: see text]1)-dimensional nonlinear evolution equation is studied via the Hirota method. Soliton, lump, breather and rogue wave, as four types of localized waves, are derived. The obtained N-soliton solutions are dark solitons with some constrained parameters. General breathers, line breathers, two-order breathers, interaction solutions between the dark soliton and general breather or line breather are constructed by choosing suitable parameters on the soliton solution. By the long wave limit method on the soliton solution, some new lump and rogue wave solutions are obtained. In particular, dark lumps, interaction solutions between dark soliton and dark lump, two dark lumps are exhibited. In addition, three types of solutions related with rogue waves are also exhibited including line rogue wave, two-order line rogue waves, interaction solutions between dark soliton and dark lump or line rogue wave.

New Optical Soliton Solutions for Coupled Resonant Davey-Stewartson System with Conformable Operator

2021 ◽  
Author(s):  
Shrideh Al-Omari ◽  
Mohammed Alabedalhadi ◽  
Mohammed Al-Smadi ◽  
Shaher Momani
Keyword(s):  
Soliton Solutions ◽  
Rational Functions ◽  
Dark Soliton ◽  
Wave Transformation ◽  
Order System ◽  
The Novel ◽  
Integer Order ◽  
Governing System ◽  
Conformable Derivatives ◽  
Fractional Orders

Abstract This paper investigates the novel soliton solutions of the coupled fractional system of the resonant Davey-Stewartson equations. The fractional derivatives are considered in terms of conformable sense. Accordingly, we utilize a complex traveling wave transformation to reduce the proposed system to an integer-order system of ordinary differential equations. The phase portrait and the equilibria of the obtained integer-order ordinary differential system will be studied. Using suitable mathematical assumptions, the new types of bright, singular, and dark soliton solutions are derived and established in view of the hyperbolic, trigonometric, and rational functions of the governing system. To achieve this, illustrative examples of the fractional Davey-Stewartson system are provided to demonstrate the feasibility and reliability of the procedure used in this study. The trajectory solutions of the traveling waves are shown explicitly and graphically. The effect of conformable derivatives on behavior of acquired solutions for different fractional orders is also discussed. By comparing the proposed method with the other existing methods, the results show that the execute of this method is concise, simple, and straightforward. The results are useful for obtaining and explaining some new soliton phenomena.

scholarly journals Dark soliton solutions to (2 + 1)-dimensional Kundu-Mukherjee-Naskar equation via the first integral method

2020 ◽  
Vol 8 (2) ◽  
pp. 40
Author(s):  
Salam Subhaschandra Singh
Keyword(s):  
Soliton Solution ◽  
Integral Method ◽  
Soliton Solutions ◽  
First Integral ◽  
Dark Soliton ◽  
Optical Soliton ◽  
Nls Equation ◽  
First Integral Method ◽  
Nonlinear Schrödinger ◽  
Trigonometric Solution

 In the present work, the First Integral Method is being applied in finding a non-soliton as well as a soliton solution of the ( 2 + 1 ) dimensional Kundu-Mukherjee-Naskar (KMN) equation which is a variant of the well-known Nonlinear Schrodinger ( NLS ) equation. Using the method, a dark optical soliton solution and a periodic trigonometric solution to the KMN equation have been suggested and the relevant conditions which guarantee the existence of such solutions are also indicated therein.  

Dark soliton solution of Sasa-Satsuma equation

2010 ◽  
Author(s):  
Y. Ohta ◽  
Wen Xiu Ma ◽  
Xing-biao Hu ◽  
Qingping Liu
Keyword(s):  
Soliton Solution ◽  
Dark Soliton

scholarly journals The Evolutionary Properties on Solitary Solutions of Nonlinear Evolution Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Wenxia Chen ◽  
Danping Ding ◽  
Xiaoyan Deng ◽  
Gang Xu
Keyword(s):  
Soliton Solution ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
Evolution Process ◽  
Solution Curve ◽  
Solitary Solutions ◽  
Basic Calculus

The evolution process of four class soliton solutions is investigated by basic calculus theory. For any given x, we describe the special curvature evolution following time t for the curve of soliton solution and also study the fluctuation of solution curve.

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