Extended Calogero-Bogoyavlenskii-Schiff equation and its dynamical behaviors

Ali, Karmina K.; Yılmazer, Reşat; Osman, M. S.

doi:10.1088/1402-4896/ac35c5

Cited by 21 publications

(3 citation statements)

References 59 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Each of these methods has its characteristics, and the simplified Hirota method is commonly used owing to its efficiency and directness. In [19][20][21][22][23][24][25][26][27][28], the authors have constructed multiple solitons, complexiton solutions, fusions, breather solutions, lump solutions, and mixed kink-lump and periodic lump solutions of some NPDEs by using the simplified Hirota's method. ) stands for the wave amplitude.…”

Section: Introductionmentioning

confidence: 99%

Dynamical rational solutions and their interaction phenomena for an extended nonlinear equation

Ali

Yusuf²,

2023

Commun. Theor. Phys.

Self Cite

View full text Add to dashboard Cite

In this paper, we analyze the extended Bogoyavlenskii-Kadomtsev-Petviashvili (eBKP) equation utilizing the condensed Hirota's approach. In accordance with a logarithmic derivative transform, we produce solutions for single, double, and triple M-lump waves. Additionally, we investigate the interaction solutions of a single M-lump with a single soliton, a single M-lump with a double soliton, and a double M-lump with a single soliton. Furthermore, we create sophisticated single, double, and triple complex soliton wave solutions. The extended Bogoyavlenskii-Kadomtsev-Petviashvili equation describes nonlinear wave phenomena in fluid mechanics, plasma, and shallow water theory. By selecting appropriate values for the related free parameters, we also create three-dimensional surfaces and associated counter plots to simulate the dynamical characteristics of the solutions offered.

show abstract

Section: Introductionmentioning

confidence: 99%

Dynamical rational solutions and their interaction phenomena for an extended nonlinear equation

Ali

Yusuf²,

2023

Commun. Theor. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…)-expansion method, etc. In [29], the dynamics of Riemann waves have been investigated. In [30], lump solutions of the extended Calogero-Bogoyavlenskii-Schiff equation which involves three fourth-order terms has been studied.…”

Section: Introductionmentioning

confidence: 99%

Analytical solutions of (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff equation in fluid mechanics/plasma physics using the New Kudryashov method

2022

View full text Add to dashboard Cite

This study investigates various analytic soliton solutions of the generalized (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (CBS) equation in fluid dynamics and plasma physics using a recently introduced technique which is the New Kudryashov method. Moreover, it is examined how the wave propagation in both directions represented by the CBS equation occurs. The considered equation describes the interaction of the long propagating wave in the x axis with the Riemann propagating wave along the y axis. To get traveling wave solutions of the CBS equation, it is transformed into a nonlinear ordinary differential equation (NLODE) using a proper wave transformation. Supposing that the NLODE has some solutions in the form provided by the method, one can obtain a nonlinear system of algebraic equations. The unknowns in the system can be found by solving the system via computer algebraic systems such as Mathematica and Maple, etc. Substituting the unknowns into the trial solutions provided by the method, we get the solutions of the NLODE. Then, putting wave transformations back into the solutions of NLODE, we get the solutions of the considered CBS equation. We present the 2D, 3D and contour plots to illustrate the physical behavior of the obtained solutions using the appropriate parameters. Besides, the schematic representation of wave motion of the soliton along both spatial axes and its interpretation are given. The used novel technique can be used for a wide range of partial differential equations (PDEs) in the real world. It is expected that the derived soliton solutions might be helpful for better understanding the wave behavior and so, it might contribute to future studies in various disciplines.

show abstract

“…However, there is no report on whether the Hirota's method [14,[35][36][37][38][39][40], as a direct method to obtain the exact solution of the integrable system, can derive the multiple-pole solution of FNLS equation. According to the bilinear method, the N-soliton solution of the FNLS equation takes the following form [19,20,41]:…”

Section: Introductionmentioning

confidence: 99%

Multiple-pole solutions and degeneration of breather solutions to the focusing nonlinear Schrödinger equation

Zhang¹,

Chen²,

Guo³

2022

Commun. Theor. Phys.

View full text Add to dashboard Cite

Based on Hirota’s method, the multiple-pole solutions of the focusing Schrödinger equation are derived directly by introducing some new ingenious limit methods. We have carefully investigated these multi- pole solutions from three perspectives: rigorous mathematical expressions, vivid images, and asymp- totic behavior. Moreover, there are two kinds of interactions between multi-pole solutions: when two multiple-pole solutions have different velocities, they will collide for a short time; when two multiple- pole solutions have very close velocities, a long time coupling will occur. The last important point is that this method of obtaining multiple-pole solutions can also be used to derive degeneration of N-breather solutions. The method mentioned in this paper can be extended to derivative Schr¨odinger equation, Sine-Gorden equation, mKdV equation and so on.

show abstract

Extended Calogero-Bogoyavlenskii-Schiff equation and its dynamical behaviors

Cited by 21 publications

References 59 publications

Dynamical rational solutions and their interaction phenomena for an extended nonlinear equation

Dynamical rational solutions and their interaction phenomena for an extended nonlinear equation

Analytical solutions of (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff equation in fluid mechanics/plasma physics using the New Kudryashov method

Multiple-pole solutions and degeneration of breather solutions to the focusing nonlinear Schrödinger equation

Contact Info

Product

Resources

About