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

Xu, Hang; Cheng, Wen‐Hao; Cui, Jifeng

doi:10.1140/epjs/s11734-021-00374-9

Cited by 3 publications

(2 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Allowing the approximate solutions u x, t and v x, t given by Eqs. (11) and (12) to satisfy the boundary conditions (Eq. ( 4)) and eliminating γ −2 t , γ −1 t ,…”

Section: Derivation Methodsmentioning

confidence: 99%

“…Its fractional counterpart describes shallow water in a porous medium, which can absorb wave energy and prevent tsunamis. Several analytical and numerical methods have been developed to solve the WBK equations [11][12][13][14]. Wang and Chen [15] applied an analytic iterative technique called the residual power series method to solve time-fractional WBK equations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

“…Allowing the approximate solutions u x, t and v x, t given by Eqs. (11) and (12) to satisfy the boundary conditions (Eq. ( 4)) and eliminating γ −2 t , γ −1 t ,…”

Section: Derivation Methodsmentioning

confidence: 99%

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

show abstract

Bursting oscillations, bifurcation delay and multi-stability in complex nonlinear systems

Wei

Rajagopal

Qian

2022

Eur. Phys. J. Spec. Top.

View full text Add to dashboard Cite

Nonlinear dynamics of soliton molecules, hybrid interactions and other wave solutions for the (3+1)-dimensional generalized Kadomtsev–Petviashvili–Boussinesq equation

Wang,

Shi

2024

Mod. Phys. Lett. B

View full text Add to dashboard Cite

This work plumbs the nonlinear dynamics of the ([Formula: see text])-dimensional generalized Kadomtsev–Petviashvili–Boussinesq equation (gKPBe), which is used to describe some interesting physical phenomena in the fields of fluids. The resonance conditions of the soliton molecules on the ([Formula: see text]), ([Formula: see text]) and ([Formula: see text]) planes are investigated and the soliton molecules are obtained on the basis of the N-soliton solutions that are extracted by virtue of the Hirota form. Furthermore, some novel hybrid interactions including the interaction between the soliton and soliton molecule, the interaction between the different soliton molecules are also explored. Finally, the sub-equation approach is exerted to explore the various wave solutions, which include the kinky wave, bright-dark wave and the singular periodic wave solutions. Correspondingly, the graphical descriptions of the attained solutions are drawn to present a better understanding of the physical attributes. The derived solutions can enlarge the exact solutions of the ([Formula: see text])-dimensional gKPBe and lead us to understand the nonlinear dynamic behaviors better.

show abstract

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

Cited by 3 publications

References 29 publications

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

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

Bursting oscillations, bifurcation delay and multi-stability in complex nonlinear systems

Nonlinear dynamics of soliton molecules, hybrid interactions and other wave solutions for the (3+1)-dimensional generalized Kadomtsev–Petviashvili–Boussinesq equation

Contact Info

Product

Resources

About