Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation

Avazzadeh, Z.; Nikan, O.; Machado, J. A. Tenreiro

doi:10.3390/math8091601

Cited by 32 publications

(6 citation statements)

References 57 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The gKdV equation and the dispersive-Fisher equation could be easily obtained by taking r = 0 and ò = 0 in the given equation, respectively [5]. Since it is hard to catch their exact solutions analytically, many numerical methods have been performed gradually [9,20].…”

Section: Model Description and Methodologymentioning

confidence: 99%

See 1 more Smart Citation

A discretization-free deep neural network-based approach for advection-dispersion-reaction mechanisms

Uslu Tuna,

Sari,

Cosgun

2024

Phys. Scr.

View full text Add to dashboard Cite

This study aims to provide insights into new areas of artificial intelligence approaches by examining how these techniques can be applied to predict behaviours for difficult physical processes represented by partial differential equations, particularly equations involving nonlinear dispersive behaviours. The current advection-dispersion-reaction equation is one of the key formulas used to depict natural processes with distinct characteristics. It is composed of a first-order advection component, a third-order dispersion term, and a nonlinear response term. Using the deep neural network approach and accounting for physics-informed neural network awareness, the problem has been elaborately discussed. Initial and boundary conditions are added as constraints when the neural networks are trained by minimizing the loss function. In comparison to the existing results, the approach has produced qualitatively correct kink and anti-kink solutions, with losses often remaining around 0.01%. It has also outperformed several traditional discretization-based methods.

show abstract

Section: Model Description and Methodologymentioning

confidence: 99%

“…In this concept, kink and anti-kink solutions of ADR equations are prominent in models of dispersive behaviour. A variety of models, such as the sine-Gordon equation, the generalized Korteweg-de Vries equation (gKdV) equation, the linear Schrodinger equation, and nonlinear Klein-Gordon equations have kink solutions [2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

A discretization-free deep neural network-based approach for advection-dispersion-reaction mechanisms

Uslu Tuna,

Sari,

Cosgun

2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…The meshfree RBF method is used in both local and global forms. Some authors have tried localized-RBF-based strategies, such as the localized-RBF-generated FD (RBF-FD) [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 ] and the RBF partition of unity (RBF-PU) [ 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 ].…”

Section: Properties Of Rbfsmentioning

confidence: 99%

Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method

Golbabai

Safaei

Molavi-Arabshahi

2022

Entropy

View full text Add to dashboard Cite

This paper introduces a direct method derived from the global radial basis function (RBF) interpolation over arbitrary collocation nodes occurring in variational problems involving functionals that depend on functions of a number of independent variables. This technique parameterizes solutions with an arbitrary RBF and transforms the two-dimensional variational problem (2DVP) into a constrained optimization problem via arbitrary collocation nodes. The advantage of this method lies in its flexibility in selecting between different RBFs for the interpolation and parameterizing a wide range of arbitrary nodal points. Arbitrary collocation points for the center of the RBFs are applied in order to reduce the constrained variation problem into one of a constrained optimization. The Lagrange multiplier technique is used to transform the optimization problem into an algebraic equation system. Three numerical examples indicate the high efficiency and accuracy of the proposed technique.

show abstract

“…However, analytical modeling is a useful tool to verify numerical models of groundwater problems. Also, mathematical models include numerical methods have been investigated by several researchers (Avazzadeh et al 2020;Nikan and Avazzadeh 2021;Nikan et al 2022;Rasoulizadeh et al 2021).…”

Section: Introductionmentioning

confidence: 99%

Modeling the river-aquifer via a new exact model under a more general function of river water level variation

Saeedpanah

Azar

2023

Appl Water Sci

View full text Add to dashboard Cite

The interaction between surface water and groundwater is a significant topic in groundwater-related problems. This study suggests an exact model based on Laplace transformation to calculate the groundwater flow in river-aquifer systems. Exact models play an important role in simulating the future behavior of river-aquifer systems. Therefore, investigation of the exact models for river-aquifer systems is a hot topic in the hydraulics of groundwater flow modeling. The objective of this research is to present new exact models for simulating the hydraulics of groundwater flow in river-aquifer systems with a more general function of river level variation under recharge by means of Laplace transform method. A general function is adopted to describe the river level variation, in which some situations such as linear, exponential and power of time variations in the river level can be treated as special cases. The effects of variations in aquifer parameters on groundwater hydraulic head are evaluated. It is shown that the groundwater hydraulic head grows slower in aquifers with a greater thickness or hydraulic conductivity. In addition, the effect of changes in specific storage is too little on the groundwater hydraulic head. The variations in hydraulic heads due to changes in recharge rate with different values of thickness, hydraulic conductivity, specific storage, and length are analyzed. It is observed that the groundwater hydraulic head in an aquifer with a lesser length, higher hydraulic conductivity or higher thickness is less sensitive to a change in the recharge rate than in an aquifer with a higher length, lesser hydraulic conductivity or lesser thickness. Furthermore, it is shown that the differences in hydraulic heads due to the increase in recharge rate are not significant for different values of specific storage. The results of the present new exact models are successfully verified by the results obtained from the analytical solution of Bansal and Das. Also, for more reliability, the results are compared with those results of MODFLOW. The results show that the presented new exact models are accurate, robust and efficient. One of the advantages of the solutions is to investigate the sensitivity analysis of aquifer parameters, which has been carried out in this paper. Furthermore, in the present research a more general function describing river level variation is considered, in which the linear, exponential and power of time variations are special cases.

show abstract

Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation

Cited by 32 publications

References 57 publications

A discretization-free deep neural network-based approach for advection-dispersion-reaction mechanisms

A discretization-free deep neural network-based approach for advection-dispersion-reaction mechanisms

Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method

Modeling the river-aquifer via a new exact model under a more general function of river water level variation

Contact Info

Product

Resources

About