Analytical solutions of simplified modified Camassa-Holm equation with conformable and M-truncated derivatives: A comparative study

Onder, Ismail; Çinar, Melih; Seçer, Aydın; Bayram, Mustafa

doi:10.1016/j.joes.2022.06.012

Cited by 17 publications

(10 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In figure 3, we illustrate the graphs of f 1,2 (x, y, z, t) as defined in equation (10). Figure 3(a) presents a 3D plot of the solution, characterized as a singular soliton solution, with parameters…”

Section: Resultsmentioning

confidence: 99%

“…Among these PDE models, nonlinear partial differential equations (NLPDEs), which are more compatible with real-life problems, are frequently used. Motivation of the study and resources that we used can be listed as; Korteweg-de Vries (KdV) equation which models shallow water wave surfaces, some important evolution equations [1][2][3][4][5][6], Zakharov-Kuznetsov (ZK) equation [7] which models propagation of the ion-sound waves in magnetic fields, Boussinesq equation [8] which models long wave propagation in shallow water, Kadomtsev-Petviashvili (KP) equation [9] which is a natural generalization of the KdV equation and models the crossing swells occurred in Atlantic ocean, Camassa-Holm (CH) equation [10] which models shallow water wave with non-hydrostatic pressure. There are also modified, extended, or combined models of these equations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Soliton solutions of time-fractional modified Korteweg-de-Vries Zakharov-Kuznetsov equation and modulation instability analysis

Onder,

Secer,

Bayram

2023

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

In this paper, we explore analytical solutions for the (3+1)-dimensional time-fractional modified Korteweg–de Vries Zakharov-Kuznetsov equation, which incorporates a conformable derivative. Our interest in this model is driven by its significant role in simulating ion-acoustic waves in magnetized plasma. We adopt the unified Riccati equation expansion method and the new Kudrashov method to discover soliton solutions. Our approach uncovers various soliton types, such as kink, singular, periodic-singular, and bright solitons. We conduct a thorough analysis of how different parameters affect wave propagation, enhancing our study with descriptive figures and insightful observations. Furthermore, we delve into the modulation instability characteristic of this model. The influence of specific parameters, like wave number and the order of the conformable derivative, on wave dynamics is demonstrated through detailed visualizations. We also present 2D and 3D graphical representations of these solutions.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Soliton solutions of time-fractional modified Korteweg-de-Vries Zakharov-Kuznetsov equation and modulation instability analysis

Onder,

Secer,

Bayram

2023

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Considering the solution set in equation (40), wave transformation in equation (3), proposed solution form in equation (18) and relation between Ψ and Φ, we obtained the following solutions after some simplifications;…”

Section: Utilization Of Aemmentioning

confidence: 99%

“…In the literature, there are some analytical methods used to obtain soliton solutions such as, enhanced modified extended tanh expansion method [14], Sardar sub-equation method [15], new Kudryashov method [16,17], extended rational sine-cosine and sinh-cosh method [18], generalized projective Riccati equation method [19], sinh-Gordon expansion method [20], generalized F-expansion method (GFEM) [21] and auxiliary equation method (AEM) [22].…”

Section: Introductionmentioning

confidence: 99%

Soliton solutions of coupled resonant Davey-Stewartson system and modulation instability analysis

Onder¹,

Seçer²,

Bayram³

2023

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

We have discussed the perturbed Gerdjikov-Ivanov (pGI) equation describing optical pulse propagation (PP) with perturbation effects, which has various applications in optical fibers, especially in photonic crystal fibers. According to our literature review, we have discovered new and original soliton types using the Sardar sub-equation and the modified Kudryashov methods, which have not been applied to this model before. We obtained dark, bright, periodic-singular and periodic-M-shaped soliton solutions, respectively. The analytical forms of the obtained solutions are represented by 3D, 2D and contour graphics. In addition, the physical effects of the solution parameters on the wave envelope have been described and clearly interpreted by presenting their 2D graphics

show abstract

“…Authors of Reference [53] investigated the exact soliton solutions of a nonlinear Schrödinger equation including Kudryashov's sextic powerlaw nonlinearity by two efficient analytical methods. Cinar et al [54] studied the soliton solutions for the perturbed Fokas-Lenells equation which has a vital role in optics by using Sardar subequation method. In Reference [55], the analytical solutions of simplified modified Camassa-Holm equations with various derivative operators, namely, conformable and M-truncated derivatives were obtained.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Behaviors of Lumpoff and Rogue Wave Solutions for Nonlocal Gardner Equation

Manafian

Takami

Eslami

et al. 2022

Mathematical Problems in Engineering

View full text Add to dashboard Cite

In this paper, we got a novel kind of rogue waves with the predictability of (2 + 1)-dimensional nonlocal Gardner equation with the aid of Maple according to the Hirota bilinear model. We first construct a general quadratic function to derive the general lump solution for the mentioned equation. At the same time, the lumpoff solutions are demonstrated with more free autocephalous parameters, in which the lump solution is localized in all directions in space. Moreover, when the lump solution is cut by twin-solitons, special rogue waves are also introduced. Based on the data available in the literature, the resulting soliton solutions are innovative, developed, distinctive, and significant and can be applied to more complex phenomena, and they are immensely active for nonlinear models of classical and fractional-order type. To examine the dynamic behavior of the waves, contour 3D and 2D plots of several obtained findings are sketched by assigning specific values to the parameters. Furthermore, we obtain new sufficient solutions containing cross-kink, periodic-kink, multi-waves, and solitary wave solutions. It is worth noting that the emerging time and place of the rogue waves depend on the moving path of the lump solution.

show abstract

Analytical solutions of simplified modified Camassa-Holm equation with conformable and M-truncated derivatives: A comparative study

Cited by 17 publications

References 45 publications

Soliton solutions of time-fractional modified Korteweg-de-Vries Zakharov-Kuznetsov equation and modulation instability analysis

Soliton solutions of time-fractional modified Korteweg-de-Vries Zakharov-Kuznetsov equation and modulation instability analysis

Soliton solutions of coupled resonant Davey-Stewartson system and modulation instability analysis

Dynamical Behaviors of Lumpoff and Rogue Wave Solutions for Nonlocal Gardner Equation

Contact Info

Product

Resources

About