Breaking analysis of solitary waves for the shallow water wave system in fluid dynamics

Duran, Serbay; Kaya, Doǧan

doi:10.1140/epjp/s13360-021-01924-9

Cited by 27 publications

(6 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although this transformation is described in many articles to reduce a complex structure to a simpler one, the physical discussions of the parameters used in the transformation and the effect of these parameters on the process are also very important. When the literature is examined, many methods such as the simplified extended ¢ G G ( )-expansion method [9], modified expansion method [10],…”

Section: Introductionmentioning

confidence: 99%

A study on solitary wave solutions for the Zoomeron equation supported by two-dimensional dynamics

Duran,

Yokus,

Kilinc

2023

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

This study emphasizes the importance of understanding natural phenomena through various observations and relating them to scientific studies. Nonlinear partial differential equations serve as fundamental tools for modeling these phenomena, with a focus on nonlinear evolution equations when involving time. This paper investigates the dynamics of the Zoomeron equation, highlighting not only a result derived from the KdV and Schrödinger equations but also its contribution to the modeling of Boomeron and Trappon solitons. Different analytical techniques yield various solutions for the Zoomeron equation, each offering unique insights. The behavior of the solutions generated in kink and singular soliton forms in various dynamics using the G ′ / G 2 -expansion method is investigated and compared under restrictive conditions, and the distribution of energy density is explained with the assistance of the gradient function. It is aimed at gaining a physically unique perspective by revealing the connections between the velocities of solitons produced for this equation and the effects of gradient flow directions. In addition, stability analysis for some of the solutions generated in the kink form is investigated. The structure of the paper includes method introduction, application, stability property, results and discussion, resulting in a unique perspective on understanding the physical dynamics of the Zoomeron model.

show abstract

Section: Introductionmentioning

confidence: 99%

A study on solitary wave solutions for the Zoomeron equation supported by two-dimensional dynamics

Duran,

Yokus,

Kilinc

2023

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Tese kinds of dynamical information help to understand, predict, and control the complex behaviors of fnancial market. Nowadays, various powerful technical tools have been proposed to explore these NPDEs, such as inverse scattering method [20], Hirota's bilinear method [21], F-expansion method [22][23][24][25][26][27][28][29][30], and auto-Bäcklund transformation method [31].…”

Section: Introductionmentioning

confidence: 99%

Solitary Wave and Singular Wave Solutions for Ivancevic Option Pricing Model

Zeng

Liang

Yuan

2022

Mathematical Problems in Engineering

View full text Add to dashboard Cite

The nonlinear option pricing model presented by Ivancevic is investigated. By using travelling wave transforming method, the nonlinear option pricing equation is transformed into a differential equation with constant coefficients. By solving the differential equation with F-expansion method, a series of exact solutions have been obtained for the Ivancevic option pricing model. By choosing appropriate parameter values, the dark-soliton and dark-soliton-like solutions, periodic wave solutions, and rogue wave solutions are obtained. These solutions will enrich the types of exact waves in the existing literature of the Ivancevic option pricing model. Furthermore, they may have potential uses in describing the possible physical mechanisms for wave phenomenon in financial markets.

show abstract

“…The nonlinear evolution equations (NLEEs) is a very active area describing the dynamics in natural phenomena and attracted renewed interest of scientists in the theory of optical fibers phenomena arising in telecommunications, spectroscopy, plasma physics, fluid dynamics, biology, solid state physics, chemical physics, mechanics and geochemistry and many more [1][2][3][4][5][6][7][8]. The idea of soliton was first introduced in [9] and after that, a lot of work has been done to construct the soliton solution by means of many integration schemas [10,11].…”

Section: Introductionmentioning

confidence: 99%

New analytical solutions by the application of the modified double sub-equation method to the (1 + 1)-Schamel-KdV equation, the Gardner equation and the Burgers equation

2022

View full text Add to dashboard Cite

In this research we present the application of the modied double sub-equation guess solution together with the analytical solutions of the Riccati equation to obtain new analytical exact solutions to the (1+1)- Schamel-KdV equation, the (1 + 1)-dimensional Gardner equation (or combined KdV-mKdV) and the nonlinear evolution (1 + 1)-dimensional Burgers equation. Results show some conditions between the allowed values of the interaction coecients and the parameters of the allowed analytical solutions of the double sub-equation guess solution. Additionally, it has been revealed that handle the complexiton process with two dierent travelling variables have as an important consequence that the mixing between trigonometric and hyperbolic solutions is only observed for the analytical solutions of the nonlinear evolution (1 + 1)-dimensional Burgers equation, while no mixing between trigonometric and hyperbolic solutions is observed for the solutions of the (1 + 1)-Schamel-KdV ((1 + 1)-S-KdV) equation or the (1 + 1)-dimensional Gardner equation. Numerical simulations are provided in 3-D graphs and 2-D plots representing the general characteristics of the resulting analytical solutions.

show abstract

Breaking analysis of solitary waves for the shallow water wave system in fluid dynamics

Cited by 27 publications

References 41 publications

A study on solitary wave solutions for the Zoomeron equation supported by two-dimensional dynamics

A study on solitary wave solutions for the Zoomeron equation supported by two-dimensional dynamics

Solitary Wave and Singular Wave Solutions for Ivancevic Option Pricing Model

New analytical solutions by the application of the modified double sub-equation method to the (1 + 1)-Schamel-KdV equation, the Gardner equation and the Burgers equation

Contact Info

Product

Resources

About