New groups of solutions to the Whitham-Broer-Kaup equation

Wang, Yaji; Xu, Hang; Sun, Qiang

doi:10.1007/s10483-020-2683-7

Cited by 5 publications

(3 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are multiple solites for Whitham-Broer-Kaup equations, as demonstrated by Naranmandula and Chen [45]. An exact solution class was discovered by Wang et al [46], using the Whitham-Broer-Kaup equations. The Optimal Auxiliary Function Method (OAFM) can be used for the solution of a variety of different types of nonlinear differential equations.…”

Section: Introductionmentioning

confidence: 95%

Extension of the Optimal Auxiliary Function Method to Solve the System of a Fractional-Order Whitham–Broer–Kaup Equation

Alsheekhhussain,

Moaddy,

Shah

et al. 2023

Fractal Fract

View full text Add to dashboard Cite

In this paper, we introduce and implement the optimal auxiliary function method to solve a system of fractional-order Whitham–Broer–Kaup equations, a class of nonlinear partial differential equations with broad applications in mathematical physics. This method provides a systematic and efficient approach to finding accurate solutions for complex systems of fractional-order equations. We give a full analysis using tables and figures to demonstrate the reliability and accuracy of our approach. We confirm the effectiveness of our suggested method in solving the considered equations using numerical simulations and comparisons, emphasizing its potential for applications in a variety of scientific and engineering areas.

show abstract

Section: Introductionmentioning

confidence: 95%

Extension of the Optimal Auxiliary Function Method to Solve the System of a Fractional-Order Whitham–Broer–Kaup Equation

Alsheekhhussain,

Moaddy,

Shah

et al. 2023

Fractal Fract

View full text Add to dashboard Cite

show abstract

“…Wang et al [14] proposed the generalized exponential rational function method to elucidate the basic solution properties of the WBK equation. Wang et al [16] used the generalized projective Riccati equation method to solve the classical WBK equations. Yasmin [17] used the Yang decomposition method for fractional-order nonlinear WBK equations.…”

Section: Introductionmentioning

confidence: 99%

Redefined Quintic B-Spline Collocation Method to Solve the Time-Fractional Whitham-Broer-Kaup Equations

Hadhoud,

Rageh

2024

Computational and Mathematical Methods

View full text Add to dashboard Cite

This article proposes a collocation approach based on a redefined quintic B-spline basis for solving the time-fractional Whitham-Broer-Kaup equations. The presented method involves discretizing the time-fractional derivatives using an L1-approximation scheme and then approximating the spatial derivatives using the redefined quintic B-spline basis. The von Neumann technique has been used to demonstrate that the proposed method is unconditionally stable. The error estimates are discussed and show that the proposed method is third-order convergent. The results demonstrate the potential of the proposed method as a reliable tool for solving fractional differential equations.

show abstract

“…Naranmandula and Chen 19 further showed multiple soliton solutions of the Whitham-Broer-Kaup equations. Wang et al 20 captured a class of novel exact solutions of periodic, solitary, and kink types of the Whitham-Broer-Kaup equations.…”

Section: Introductionmentioning

confidence: 99%

Multiple-soliton and periodic solutions to space–time fractional Whitham–Broer–Kaup equations

Cheng

Cui

2021

Eur. Phys. J. Spec. Top.

Self Cite

View full text Add to dashboard Cite

In this paper, the space-time fractional Whitham-Broer-Kaup equations are investigated. By means of new fractional scaling transformations, the fractional nonlinear system of different time and space orders is transformed to the integer one. The multiple solitary solutions and periodic solutions are obtained respectively. All those solutions are given exactly by introducing new scaling transformations, which makes our study is unique and different from most existing studies. It is expected that exact solutions for nonlinear wave system of fractional order can be handled in the similar way.

show abstract

New groups of solutions to the Whitham-Broer-Kaup equation

Cited by 5 publications

References 22 publications

Extension of the Optimal Auxiliary Function Method to Solve the System of a Fractional-Order Whitham–Broer–Kaup Equation

Extension of the Optimal Auxiliary Function Method to Solve the System of a Fractional-Order Whitham–Broer–Kaup Equation

Redefined Quintic B-Spline Collocation Method to Solve the Time-Fractional Whitham-Broer-Kaup Equations

Multiple-soliton and periodic solutions to space–time fractional Whitham–Broer–Kaup equations

Contact Info

Product

Resources

About