Effect of Coriolis constant on Geophysical Korteweg-de Vries equation

Karunakar, Perumandla; Chakraverty, Snehashish

doi:10.1016/j.joes.2019.02.002

Cited by 35 publications

(22 citation statements)

References 28 publications

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“…It has been observed from the literature that KdV equation has been studied by various researchers in different directions [3,[24][25][26].…”

Section: Mathematical Modelingmentioning

confidence: 99%

“…To inspect influence of the Coriolis term 0 u x [28], we derive analytical wave structures of the GKdVE and collate them to the explicit structures of the KdV equation. The solitary wave solution of Equation (1) is [3] u(x, t) = asech 2…”

Section: Mathematical Modelingmentioning

confidence: 99%

“…Here, propagation of nonlinear solitary wave is examined of the GKdVE (1) by choosing the suitable conditions as u → 0 while x → ± ∞. We use the solitary wave of Equation (1) [3] as…”

Section: Solitary Wave Propagationmentioning

confidence: 99%

“…To inspect influence of the Coriolis term ω 0 u x [28], we derive analytical wave structures of the GKdVE and collate them to the explicit structures of the KdV equation. The solitary wave solution of Equation (1) is [3]

u (x, t) = a {normalsech}^{2} [k (x - ct)], 0 \leq x \leq L,

where

a = 2 (c + ω_{0}), k = \sqrt{\frac{3}{2} (c + ω_{0})} .

We move forward with a conversation on the utility of the GKdVE for tsunami waves in equatorial regions.…”

Section: Mathematical Modelingmentioning

confidence: 99%

“…The tsunami wave speed is based on depth of the ocean instead of their distance from the source of the wave. All tsunamis are drastically menacing, even if they may not mar every coastline they strike [3].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Investigation of Coriolis effect on oceanic flows and its bifurcation via geophysical Korteweg–de Vries equation

Saha

Dhawan

et al. 2020

Numerical Methods Partial

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In this work, we have investigated Coriolis effect on oceanic flows in the equatorial region with the help of geophysical Korteweg-de Vries equation (GKdVE). First, Lie symmetries and conservation laws for the GKdVE have been studied. Later, we implement finite element method for numerical simulations. Propagation of nonlinear solitary structures, their interaction and advancement of solitons can be seen in the results so produced. Additionally, Gaussian initial condition and undular bore initial condition are also investigated. Results so obtained have been found in perfect agreement with the available results. Bifurcation analysis of the oceanic traveling wave of the GKdVE is presented depending on traveling wave velocity and Coriolis parameter. It is discerned that velocity of the traveling wave and Coriolis parameter affect significantly on the propagation of the nonlinear waves.

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“…It has been observed from the literature that KdV equation has been studied by various researchers in different directions [3,[24][25][26].…”

Section: Mathematical Modelingmentioning

confidence: 99%

Section: Mathematical Modelingmentioning

confidence: 99%

Section: Solitary Wave Propagationmentioning

confidence: 99%

u (x, t) = a {normalsech}^{2} [k (x - ct)], 0 \leq x \leq L,

where

a = 2 (c + ω_{0}), k = \sqrt{\frac{3}{2} (c + ω_{0})} .

We move forward with a conversation on the utility of the GKdVE for tsunami waves in equatorial regions.…”

Section: Mathematical Modelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Investigation of Coriolis effect on oceanic flows and its bifurcation via geophysical Korteweg–de Vries equation

Saha

Dhawan

et al. 2020

Numerical Methods Partial

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Diverse general solitary wave solutions and conserved currents of a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science

Adeyemo

2024

Math Methods in App Sciences

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This article presents an analytical investigation performed on a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science. To start with, achieving diverse solitary wave solutions to the generalized power‐law model involves using wave transformation, which reduces the model to a nonlinear ordinary differential equation. A direct integration approach is adopted to construct solutions in the beginning. This brings the emergence of interesting solutions like non‐topological solitons, trigonometric functions, exponential functions, elliptic functions, and Weierstrass functions in general structures. Besides, in a bid to secure more general exact solutions to the model, one adopts the extended Jacobi elliptic function expansion technique (for some specific cases of ). Thus, various cnoidal, snoidal, and dnoidal wave solutions to the understudied model are attained. The copolar trio explicated in a tabular form reveals that these solutions can be relapsed to various hyperbolic and trigonometric functions under certain criteria. Additionally, diverse graphical exhibitions of the dynamical attributes of the gained results are presented in a bid to have a sound understanding of the physical phenomena of the underlying model. Later, one gives the conserved vectors of the aforementioned equation by employing the standard multiplier approach.

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Stability analysis and approximate solution of interval mathematical model for the COVID‐19 pandemic

Karunakar

Reddy

Chakraverty

2023

Math Methods in App Sciences

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In this paper, an interval solution has been constructed for the system of differential equations (SDEs) governing the COVID‐19 pandemic with uncertain parameters, namely, interval. The imposition of lockdown on infective has been considered as an interval parameter. As a result, the complete system of first‐order differential equations is transformed into interval form. The resulting interval system of differential equations (ISDEs) has been solved with help of the parametric concept and the Runge–Kutta method of order 4. Obtained results are compared with existing crisp results, and they are found to be in good agreement.

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Effect of Coriolis constant on Geophysical Korteweg-de Vries equation

Cited by 35 publications

References 28 publications

Investigation of Coriolis effect on oceanic flows and its bifurcation via geophysical Korteweg–de Vries equation

Investigation of Coriolis effect on oceanic flows and its bifurcation via geophysical Korteweg–de Vries equation

Diverse general solitary wave solutions and conserved currents of a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science

Stability analysis and approximate solution of interval mathematical model for the COVID‐19 pandemic

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