Results 41 to 50 of about 23,042 (190)

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

Exact solutions for the nonlinear extended KdV equation in a stratified shear flow using modified exponential rational method

Results in Physics, 2021
In this article, we study the nonlinear higher order of extended KdV equation with free surface displacement. The modified exponential rational function method is used in order to find exact solutions of the extended KdV equation.
Ali Althobaiti, Saad Althobaiti, K. El-Rashidy, Aly R. Seadawy   +3 more
doaj   +1 more source

Unidirectional wave motion in a nonlocally and nonlinearly elastic medium: the KdV, BBM, and CH equations; pp. 256–262 [PDF]

Proceedings of the Estonian Academy of Sciences, 2015
We consider unidirectional wave propagation in a nonlocally and nonlinearly elastic medium whose constitutive equation is given by a convolution integral with a suitable kernel function.
Hüsnü Ata Erbay, Saadet Erbay, Albert Erkip   +2 more
doaj   +1 more source

Conformal Properties and Baecklund Transform for the Associated Camassa-Holm Equation [PDF]

, 2005
Integrable equations exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants. The most basic and important example is the KdV equation and the corresponding Schwarz-KdV equation.
Beals, Beals, Bol, Camassa, Constantin, Constantin, Constantin, Constantin, Constantin, Constantin, Constantin, Depireux, Dickey, Dorfman, Fisher, Fokas, Fokas, Galas, Gieres, Hille, Hone, Hone, Johnson, Johnson, Lenells, Lou, Matveev, Matveev, Matveev, Matveev, Matveev, Misiolek, Nucci, Rasinariu, Rossen Ivanov, Schiff, Schiff, Shabat, Weiss, Weiss, Wilson   +40 more
core   +4 more sources

Fredholm Determinant and Wronskian Representations of the Solutions to the Schrödinger Equation with a KdV-Potential

Axioms
From the finite gap solutions of the KdV equation expressed in terms of abelian functions we construct solutions to the Schrödinger equation with a KdV potential in terms of fourfold Fredholm determinants.
Pierre Gaillard
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

Integrable Extensions of N=2 Supersymmetric KdV Hierarchy Associated with the Nonuniqueness of the Roots of the Lax operator

, 1998
We preesent a new supersymmetric integrable extensions of the a=4,N=2 KdV hierarchy. The root of the supersymmetric Lax operator of the KdV equation is generalized, by including additional fields.
Ablowitz, Bellucci, Belluci, Brezin, Chaichian, Dargis, Das, Delduc, Delduc, Faddeev, Gross, Inami, Ivanov, Kulish, Labelle, Laberge, Manin, Mathieu, Oevel, Polyakov, Popowicz, Popowicz, Popowicz, Yung, Z. Popowicz   +24 more
core   +2 more sources

Rational approximate symmetries of KdV equation [PDF]

Journal of Physics A: Mathematical and General, 2003
We construct one-parameter deformation of the Dorfman Hamiltonian operator for the Riemann hierarchy using the quasi-Miura transformation from topological field theory. In this way, one can get the approximately rational symmetries of KdV equation and then investigate its bi-Hamiltonian structure.
openaire   +3 more sources

Free Surface Waves in Electrohydrodynamics With a Prescribed Vorticity Distribution

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT Traditionally, the study of free surface flows assumed irrotationality to simplify matters, and the results seemed to have great success, notably with the Korteweg‐de Vries(KdV) equation. In the past decade, there have been attempts to remove this seemingly strong condition and replace it with a global constant vorticity equivalent to a linear
M. J. Hunt, Denys Dutykh
wiley   +1 more source

Analytical and Numerical Soliton Solutions of the Shynaray II‐A Equation Using the G′G,1G$$ \left(\frac{G^{\prime }}{G},\frac{1}{G}\right) $$‐Expansion Method and Regularization‐Based Neural Networks

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT Nonlinear differential equations play a fundamental role in modeling complex physical phenomena across solid‐state physics, hydrodynamics, plasma physics, nonlinear optics, and biological systems. This study focuses on the Shynaray II‐A equation, a relatively less‐explored parametric nonlinear partial differential equation that describes ...
Aamir Farooq, H. W. A. Riaz, Sadique Rehman, M. Mamun Miah, Wen Xiu Ma   +4 more
wiley   +1 more source