On controlled propagation of long waves in nonautonomous Boussinesq–Burgers equations

The generalized fractional Caputo‐operator is discussed. The reduction of partial differential equations retarded or advanced with delays is obtained. The applications to the space‐time‐fractional KdV and time‐fractional Boussenisq‐Burger's equation are carried. Semi‐self‐similar SS wave solutions are obtained. That is, there exists a soliton wave propagates along a specific characteristic curve in the xt‐ plane. This may be due to the effects associated with the distributed time delay. The effects of space fractional derivative on a system are attributed to the transition states. Thus, anomalous wave transport is produced mainly near the origin.

show abstract

“…We solve Equation by using the unified method . For polynomial solutions, we write

U false(z false) = true \sum_{j = 0}^{j = n} a_{j} g^{j} false(z false), {false(g^{'} false(z false) false)}^{p} = true \sum_{j = 0}^{j = k} c_{j} g^{j} false(z false),

where

p = 1

, the auxiliary equation solves to elementary fiction or implicit functions.…”

Section: Applicationsmentioning

confidence: 99%

“…We solve Equation (28) by using the unified method. [39][40][41][42][43][44] For polynomial solutions, we write…”

Section: Consider the Space-time-fractional Kdv Equationmentioning

confidence: 99%

Fractional KdV and Boussenisq‐Burger's equations, reduction to PDE and stability approaches

2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…This case represents more realistic models than those which are considered with constant coefficients . The soliton wave propagation in the above‐mode has been called “non‐autonomous soliton.” Hence, N‐soliton nonautonomous soliton interactions in various play a definitive role in the formation of the structure of wave and also the propagation direction with a phase shift in dispersive media …”

Section: Introductionmentioning

confidence: 99%

“…Hence, N-soliton nonautonomous soliton interactions in various play a definitive role in the formation of the structure of wave and also the propagation direction with a phase shift in dispersive media. [18][19][20][21][22][23][24] The dispersive long (surface) water waves with time-dependent coefficient are given by the equations…”

Section: Introductionmentioning

confidence: 99%

On multiple soliton similariton‐pair solutions, conservation laws via multiplier and stability analysis for the Whitham–Broer–Kaup equations in weakly dispersive media

Abdel‐Gawad

Tantawy

Yusuf

2019

Math Methods in App Sciences

View full text Add to dashboard Cite

In this article, the generalized unified method (GUM) is used for finding multiwave solutions of the coupled Whitham‐Broer‐Kaup (WBK) equation with variable coefficients. Which describes the propagation of of shallow water waves. Here, we study the effects of the indirect nonlinear interaction of one‐, two‐ and three‐solitonic similaritons on the behavior of propagation of waves, in quasi‐periodic distributed system. This study can unable us to control the dynamics of type soliton (soliton, anti‐soliton) similaritons waves in dispersive waveguides. To give more physical insight to the obtained solutions, they are shown graphically. Their different structures are depicted by taking appropriate arbitrary functions. Further, with the suitable parameters, the indirect nonlinear interaction between two and three‐soliton waves are shown weal, in the sense that their amplitude does not blow up. Moreover, because of the importance of conservation laws Cls and stability analysis SA in the investigation of integrability, internal properties, existence, and uniqueness of a differential equation, we compute the Cls via multiplier technique and stability analysis via the concept of linear stability analysis for the WBK equations using the constant coefficients.

show abstract

On $$\varvec{N}$$ N -mixed-type soliton propagation in dispersive nonautonomous long waves with waveguides

Abdel‐Gawad

Tantawy

2017

Nonlinear Dyn

View full text Add to dashboard Cite

On controlled propagation of long waves in nonautonomous Boussinesq–Burgers equations

Cited by 9 publications

References 42 publications

Fractional KdV and Boussenisq‐Burger's equations, reduction to PDE and stability approaches

Fractional KdV and Boussenisq‐Burger's equations, reduction to PDE and stability approaches

On multiple soliton similariton‐pair solutions, conservation laws via multiplier and stability analysis for the Whitham–Broer–Kaup equations in weakly dispersive media

On $$\varvec{N}$$ N -mixed-type soliton propagation in dispersive nonautonomous long waves with waveguides

Contact Info

Product

Resources

About