Dark and bright soliton solutions and computational modeling of nonlinear regularized long wave model

2021 ◽  
Vol 104 (1) ◽  
pp. 661-682 ◽  
Author(s):  
Sanjay Kumar ◽  
Ram Jiwari ◽  
R. C. Mittal ◽  
Jan Awrejcewicz
Author(s):  
S. Saha Ray ◽  
Shailendra Singh

The governing equations for fluid flows, i.e. Kadomtsev–Petviashvili–Benjamin–Bona–Mahony (KP-BBM) model equations represent a water wave model. These model equations describe the bidirectional propagating water wave surface. In this paper, an auto-Bäcklund transformation is being generated by utilizing truncated Painlevé expansion method for the considered equation. This paper determines the new bright soliton solutions for [Formula: see text] and [Formula: see text]-dimensional nonlinear KP-BBM equations. The simplified version of Hirota’s technique is utilized to infer new bright soliton solutions. The results are plotted graphically to understand the physical behavior of solutions.


2021 ◽  
pp. 2150484
Author(s):  
Asif Yokuş

In this study, the auxiliary equation method is applied successfully to the Lonngren wave equation. Bright soliton, bright–dark soliton solutions are produced, which play an important role in the distribution and distribution of electric charge. In the conclusion and discussion section, the effect of nonlinearity term on wave behavior in bright soliton traveling wave solution is examined. The advantages and disadvantages of the method are discussed. While graphs representing the stationary wave are obtained, special values are given to the constants in the solutions. These graphs are presented as 3D, 2D and contour.


Wave Motion ◽  
2016 ◽  
Vol 65 ◽  
pp. 156-174 ◽  
Author(s):  
R.M. Vargas-Magaña ◽  
P. Panayotaros

2018 ◽  
Vol 32 (06) ◽  
pp. 1850082
Author(s):  
Ding Guo ◽  
Shou-Fu Tian ◽  
Li Zou ◽  
Tian-Tian Zhang

In this paper, we consider the (3[Formula: see text]+[Formula: see text]1)-dimensional modified Korteweg–de Vries–Kadomtsev–Petviashvili (mKdV-KP) equation, which can be used to describe the nonlinear waves in plasma physics and fluid dynamics. By using solitary wave ansatz in the form of sech[Formula: see text] function and a direct integrating way, we construct the exact bright soliton solutions and the travelling wave solutions of the equation, respectively. Moreover, we obtain its power series solutions with the convergence analysis. It is hoped that our results can provide the richer dynamical behavior of the KdV-type and KP-type equations.


Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 341 ◽  
Author(s):  
Juan Luis García Guirao ◽  
Haci Mehmet Baskonus ◽  
Ajay Kumar

This paper applies the sine-Gordon expansion method to the extended nonlinear (2+1)-dimensional Boussinesq equation. Many new dark, complex and mixed dark-bright soliton solutions of the governing model are derived. Moreover, for better understanding of the results, 2D, 3D and contour graphs under the strain conditions and the suitable values of parameters are also plotted.


2020 ◽  
pp. 2150138
Author(s):  
Hajar F. Ismael ◽  
Aly Seadawy ◽  
Hasan Bulut

In this paper, we consider the shallow water wave model in the (2+1)-dimensions. The Hirota simple method is applied to construct the new dynamics one-, two-, three-, [Formula: see text]-soliton solutions, complex multi-soliton, fusion, and breather solutions. By using the quadratic function, the one-lump, mixed kink-lump and periodic lump solutions to the model are obtained. The Hirota bilinear form variable of this model is derived at first via logarithmic variable transform. The physical phenomena to this model are explored. The obtained results verify the proposed model.


2020 ◽  
pp. 2150057
Author(s):  
Xin-Mei Zhou ◽  
Shou-Fu Tian ◽  
Ling-Di Zhang ◽  
Tian-Tian Zhang

In this work, we investigate the (2+1)-dimensional generalized Bogoyavlensky–Konopelchenko (gBK) equation. Based on its bilinear form, the [Formula: see text]th-order breather solutions of the gBK equation are successful given by taking appropriate parameters. Furthermore, the [Formula: see text]th-order lump solutions of the gBK equation are obtained via the long-wave limit method. In addition, the semi-rational solutions are generated to reveal the interaction between lump solutions, soliton solutions, and breather solutions.


2018 ◽  
Vol 22 ◽  
pp. 01056 ◽  
Author(s):  
Seyma Tuluce Demiray ◽  
Hasan Bulut

In this paper, generalized Kudryashov method (GKM) is used to find the exact solutions of (1+1) dimensional nonlinear Ostrovsky equation and (4+1) dimensional Fokas equation. Firstly, we get dark and bright soliton solutions of these equations using GKM. Then, we remark the results we found using this method.


MRS Advances ◽  
2019 ◽  
Vol 4 (11-12) ◽  
pp. 667-674 ◽  
Author(s):  
Rachel N. Evans ◽  
Seth R. Calhoun ◽  
Jonathan R. Brescia ◽  
Justin W. Cleary ◽  
Evan M. Smith ◽  
...  

ABSTRACTMetal–insulator–metal (MIM) resonant absorbers comprise a conducting ground plane, a dielectric of thickness t, and thin separated metal top-surface structures of dimension l. The fundamental resonance wavelength is predicted by an analytic standing-wave model based on t, l, and the dielectric refractive index spectrum. For the dielectrics SiO2, AlN, and TiO2, values for l of a few microns give fundamental resonances in the 8-12 μm long-wave infrared (LWIR) wavelength region. Agreement with theory is better for t/l exceeding 0.1. Harmonics at shorter wavelengths were already known, but we show that there are additional resonances in the far-infrared 20 - 50 μm wavelength range in MIM structures designed to have LWIR fundamental resonances. These new resonances are consistent with the model if far-IR dispersion features in the index spectrum are considered. LWIR fundamental absorptions are experimentally shown to be optimized for a ratio t/l of 0.1 to 0.3 for SiO2- and AlN-based MIM absorbers, respectively, with TiO2-based MIM optimized at an intermediate ratio.


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