The new types of wave solutions of the Burger's equation and the Benjamin–Bona–Mahony equation

Huda, Azmol; Akbar, M. Ali; Shanta, Shewli Shamim

doi:10.1016/j.joes.2017.11.002

Cited by 15 publications

(2 citation statements)

References 46 publications

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“…the simplified Hirota's technique [24], The Wentzel-Kramers-Brillouin asymptotic method [25], Darboux transformation [26], the conformable sub-equation method [27], the improved system technique [28], the modified extended direct algebraic method [29], the linear superposition principle [30], tanh-sech method and modified Kudryashov method [31], the two variable (G'/G, 1/G)-expansion [32], a variation of parameters method (VPM) and Adomian's decomposition method (ADM) [33], the invariant subspace scheme [34], q-homotopy analysis method and Sumudu transform [35], modified versions of variational iteration algorithms [36], the standard B-spline collocation method [37] and well-known many others.…”

Section: Introductionmentioning

confidence: 99%

On the soliton solutions to some system of complex coupled nonlinear models and the effect of the coupling coefficients

Ozisik,

Esen,

Secer

et al. 2024

Preprint

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In this work, we take into account the (2 + 1)-Davey Stewartson equation (DSE) and (2 + 1)-Complex Coupled Maccari System (CCMS) and their analytical solutions. Besides, we tackle with the role of the problem parameters on the soliton behavior which the investigated DSE produces. Exact traveling wave solutions are highly useful in numerical and analytical theories in such equations. We use an efficient analytical approach to calculate the soliton solutions of these models. We have shown that soliton solutions’ features can represent the spread of propagation on the wave fronts and show a reasonable dependency on parameter values. Some of the solutions discovered in three and two-dimensional arrangements can also be described in graphic representations for their behavior. The results show that the technique is easy applicable, efficient, reliable, robust and categorical when it comes to find exact solutions for different nonlinear models. Moreover, the problem parameters and the coupling coefficients have significant effects on the behavior of the solitons of the DSE and this examination is studied for the first time in this article.

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Section: Introductionmentioning

confidence: 99%

On the soliton solutions to some system of complex coupled nonlinear models and the effect of the coupling coefficients

Ozisik,

Esen,

Secer

et al. 2024

Preprint

View full text Add to dashboard Cite

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“…Burger's equation plays a major role in the study of nonlinear waves since it is used as a mathematical model in turbulence problems, in the theory of shock waves, and in continuous stochastic processes [30]. Hopf-Cole transformation and a reproducing kernel function method, a semi-analytical iterative method, (G /G, 1/G)expansion method have been applied to the Burger's equation [31][32][33].…”

Section: Introductionmentioning

confidence: 99%

SITEM for the Conformable Space-Time Fractional (2+1)-Dimensional Breaking Soliton, Third-Order KdV and Burger's Equations

Yaslan

2021

Mathematical Sciences and Applications E-Notes

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In the present paper, new analytical solutions for the conformable space-time fractional (2+1)-dimensional breaking soliton, third-order KdV and Burger's equations are obtained by using the simplified tan( φ(ξ)2 )expansion method (SITEM). Here, fractional derivatives are described in conformable sense. The obtained traveling wave solutions are expressed by the trigonometric, hyperbolic, exponential and rational functions. Simulation of the obtained solutions are given at the end of the paper.

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Study of dynamical behavior of Burgers' equation in quantum modeling

Gupta

Shukla

Singh

2023

Math Methods in App Sciences

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Our main goal is to investigate the dynamical behavior of the quantum model of Bateman–Burgers equation utilizing a new hybrid semidiscretization technique: nCB‐DQT‐RK scheme. The nCB‐DQT‐RK is traditional differential quadrature technique (DQT) with newly modified cubic B‐splines (nCB), as a basis, which have been utilized for the discretization of spatial derivatives, and the time integration scheme SSP‐RK for the temporal discretization. The efficiency/effectiveness of the reported nCB‐DQT‐RK results, computationally, are illustrated not only numerically but also graphically for better cognizance and reliable performance of the nCB‐DQT‐RK. This is validated based on the estimation of evaluated accuracy by means of stability and convergence analysis, which infer that the proposed nCB‐DQT‐RK scheme is capable of producing stable results with spatial convergence of order four, and the use of nCB in DQT is capable to improve performance (in terms of accuracy and spatial rate of convergence as well) as compared to existing techniques (collocation/quadrature) with traditional cubic B‐splines and its existing modifications, and so, nCB is capable to surpass cubic B‐splines and its existing modification.

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The new types of wave solutions of the Burger's equation and the Benjamin–Bona–Mahony equation

Cited by 15 publications

References 46 publications

On the soliton solutions to some system of complex coupled nonlinear models and the effect of the coupling coefficients

On the soliton solutions to some system of complex coupled nonlinear models and the effect of the coupling coefficients

SITEM for the Conformable Space-Time Fractional (2+1)-Dimensional Breaking Soliton, Third-Order KdV and Burger's Equations

Study of dynamical behavior of Burgers' equation in quantum modeling

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