Results 31 to 40 of about 23,327 (208)

Exact analytical solution of viscous Korteweg-deVries equation for water waves [PDF]

, 2016
The evolution of a solitary wave with very weak nonlinearity which was originally investigated by Miles [4] is revisited. The solution for a one-dimensional gravity wave in a water of uniform depth is considered.
Sajjadi, S. G., Smith, T. A.
core   +3 more sources

Time-fractional generalized fifth-order KdV equation: Lie symmetry analysis and conservation laws

Frontiers in Physics, 2023
The purpose of this study is to apply the Lie group analysis method to the time-fractional order generalized fifth-order KdV (TFF-KdV) equation. We examine applying symmetry analysis to the TFF-KdV equation with the Riemann–Liouville (R–L) derivative ...
Zhenli Wang, Liangji Sun, Rui Hua, Lingde Su, Lihua Zhang   +4 more
doaj   +1 more source

Lie symmetry based-analytical and numerical approach for modified Burgers-KdV equation

Results in Physics, 2018
In this work, the variable-coefficient modified Burgers-KdV equation, which arises in modeling various physical phenomena, is studied for exact and numerical solution based on Lie symmetry.
Vikas Kumar, Lakhveer Kaur, Ajay Kumar, Mehmet Emir Koksal   +3 more
doaj   +1 more source

KdV-type equations linked via Baecklund transformations: remarks and perspectives

, 2018
Third order nonlinear evolution equations, that is the Korteweg-deVries (KdV), modified Korteweg-deVries (mKdV) equation and other ones are considered: they all are connected via Baecklund transformations.
Carillo, Sandra
core   +1 more source

Travelling wave solutions and conservation laws for the Korteweg-de Vries-Bejamin-Bona-Mahony equation

Results in Physics, 2018
In this work we study the Korteweg-de Vries-Benjamin-Bona-Mahony (KdV-BBM) equation, which describes the two-way propagation of waves. Using Lie symmetry method together with Jacobi elliptic function expansion and Kudryashov methods we construct its ...
Innocent Simbanefayi, Chaudry Masood Khalique   +1 more
doaj   +1 more source

On a hierarchy of nonlinearly dispersive generalized Korteweg–de Vries evolution equations; pp. 212–218 [PDF]

Proceedings of the Estonian Academy of Sciences, 2015
We propose a hierarchy of nonlinearly dispersive generalized Korteweg–de Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes.
Ivan C. Christov
doaj   +1 more source

On Symplectic and Multisymplectic Schemes for the KdV Equation [PDF]

Journal of Scientific Computing, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Uri M. Ascher, Robert I. McLachlan
openaire   +3 more sources

Time-Fractional KdV Equation: Formulation and Solution using Variational Methods

, 2011
In this work, the semi-inverse method has been used to derive the Lagrangian of the Korteweg-de Vries (KdV) equation. Then, the time operator of the Lagrangian of the KdV equation has been transformed into fractional domain in terms of the left-Riemann ...
A. A. Mahmoud, A. Babakhani, A.A. Kilbas, D. Baleanu, D. Baleanu, D. Baleanu, D. Baleanu, D. Delbosco, D.J. Korteweg, E. M. Abulwafa, E.M. Rabei, F. Riewe, F. Riewe, G.S.F. Frederico, H. Bateman, I. Podlubny, J.-H. He, J.-H. He, J.-H. He, J.-H. He, J.-H. He, J.A. Tenreiro Machado, M. A. Zahran, M. Attari, M. Inokuti, M.A.E. Herzallah, M.K. Fung, M.S. Tavazoei, N. Heymans, O.P. Agrawal, O.P. Agrawal, O.P. Agrawal, O.P. Agrawal, R.V. Mendes, R.Y. Molliq, S. A. El-Wakil, S. Momani, S. Saha Ray, S.G. Samko, S.I. Muslih, S.Q. Zhang, V.E. Tarasov, V.E. Tarasov, Y. Luchko   +43 more
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A methodological approach to solving the Korteweg–de Vries equation in its various forms

Scientific African
The Korteweg-de Vries (KdV) equation, an evolution-type nonlinear partial differential equation (PDE), describes the propagation of solitary water waves as observed in the literature.
Francis Tuffour, Benedict Barnes, Isaac Kwame Dontwi, Kwaku Forkuoh Darkwah   +3 more
doaj   +1 more source

The Solutions of Initial (-Boundary) Value Problems for Sharma-Tasso-Olver Equation

Mathematics, 2022
A nonlinear transformation from the solution of linear KdV equation to the solution of Sharma-Tasso-Olver (STO) equation is derived out by using simplified homogeneous balance (SHB) method.
Lingxiao Li, Mingliang Wang, Jinliang Zhang   +2 more
doaj   +1 more source