soliton solutions
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Sachin Kumar ◽  
Sandeep Malik ◽  
Hadi Rezazadeh ◽  
Lanre Akinyemi

Pramana ◽  
2022 ◽  
Vol 96 (1) ◽  
Kottakkaran Sooppy Nisar ◽  
Mustafa Inc ◽  
Adil Jhangeer ◽  
Muhammad Muddassar ◽  
Barka Infal

S. Şule Şener Kiliç

In this paper, we study the generalized ([Formula: see text])-dimensional Hietarinta equation which is investigated by utilizing Hirota’s bilinear method. Also, the bilinear form is obtained, and the N-soliton solutions are constructed. In addition, multi-wave and breather wave solutions of the addressed equation with specific coefficients are presented. Finally, under certain conditions, the asymptotic behavior of solutions is analyzed in both methods. Moreover, we employ the linear superposition principle to determine [Formula: see text]-soliton wave solutions for the generalized ([Formula: see text])-dimensional Hietarinta equation.

2022 ◽  
Ren Bo ◽  
Shi Kai-Zhong ◽  
Shou-Feng Shen ◽  
Wang Guo-Fang ◽  
Peng Jun-Da ◽  

Abstract In this paper, we investigate the third-order nonlinear Schr\"{o}dinger equation which is used to describe the propagation of ultrashort pulses in the subpicosecond or femtosecond regime. Based on the independent transformation, the bilinear form of the third-order NLSE is constructed. The multiple soliton solutions are constructed by solving the bilinear form. The multi-order rogue waves and interaction between one-soliton and first-order rogue wave are obtained by the long wave limit in multi-solitons. The dynamics of the first-order rogue wave, second-order rogue wave and interaction between one-soliton and first-order rogue wave are presented by selecting the appropriate parameters. In particular parameters, the positions and the maximum of amplitude of rogue wave can be confirmed by the detail calculations.PACS numbers: 02.30.Ik, 05.45.Yv.

2022 ◽  
Sachin Kumar ◽  
Nikita Mann ◽  
Harsha Kharbanda

Abstract Nonlinear evolution equations (NLEEs) are extensively used to establish the elementary propositions of natural circumstances. In this work, we study the Konopelchenko-Dubrovsky (KD) equation which depicts non-linear waves in mathematical physics with weak dispersion. The considered model is investigated using the combination of generalized exponential rational function (GERF) method and dynamical system method. The GERF method is utilized to generate closedform invariant solutions to the (2+1)-dimensional KD model in terms of trigonometric, hyperbolic, and exponential forms with the assistance of symbolic computations. Moreover, three-dimensional graphics are displayed to depict the behavior of obtained solitary wave solutions. The model is observed to have single and multiple soliton profiles, kink-wave profiles, and periodic oscillating nonlinear waves. These generated solutions have never been published in the literature. All the newly generated soliton solutions are checked by putting them back into the associated system with the soft computation via Wolfram Mathematica. Moreover, the system is converted into a planer dynamical system using a certain transformation and the analysis of bifurcation is examined. Furthermore, the quasi-periodic solution is investigated numerically for the perturbed system by inserting definite periodic forces into the considered model. With regard to the parameter of the perturbed model, two-dimensional and three-dimensional phase portraits are plotted.

2022 ◽  
Vol 2022 ◽  
pp. 1-16
Aniqa Zulfiqar ◽  
Jamshad Ahmad ◽  
Attia Rani ◽  
Qazi Mahmood Ul Hassan

The present article discovers the new soliton wave solutions and their propagation in nonlinear low-pass electrical transmission lines (NLETLs). Based on an innovative Exp-function method, multitype soliton solutions of nonlinear fractional evolution equations of NLETLs are established. The equation is reformulated to a fractional-order derivative by using the Jumarie operator. Some new results are also presented graphically to understand the real physical importance of the studied model equation. The physical interpretation of waves is represented in the form of three-dimensional and contour graphs to visualize the underlying dynamic behavior of these solutions for particular values of the parameters. Moreover, the attained outcomes are generally new for the considered model equation, and the results show that the used method is efficient, direct, and concise which can be used in more complex phenomena.

2022 ◽  
Thilagarajah Mathanaranjan

Abstract In this study, the generalized coupled nonlinear Schrodinger-KdV (NLS-KdV) system is investigated to obtain new optical soliton solutions. This system appears as a model for reciprocity between long and short waves in various of physical settings. Different kind of new soliton solutions including dark, bright, combined dark-bright, singular and combined singular soliton solutions are obtained using two effective methods namely, the extended sinh-Gordon equation expansion method and the solitary wave ansatz method. In addition, the modulation instability analysis of the system is presented based on the standard linearstability analysis. The behaviours of obtained solutions are expressed by 3D graphs.

2022 ◽  
Yajie Yang ◽  
Ying Dong

Abstract The gain or loss effect on the dynamics of the matter-wave solitons in three-component Bose-Einstein condensates with time-modulated interactions trapped in parabolic external potentials are investigated analytically. Some exact matter-wave soliton solutions to the three-coupled Gross-Pitaevskii equation describing the three-component Bose-Einstein condensates are constructed by similarity transformation. The dynamical properties of the matter-wave solitons are analyzed graphically, and the effects of the gain or loss parameter and the frequency of the external potentials on the matter-wave solitons are explored. It is shown that the gain coefficient makes the atom condensate to absorb energy from the background, while the loss coefficient brings about the collapse of the condensate.

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