Multi-wave, breather and interaction solutions to (3+ 1) dimensional Vakhnenko–Parkes equation arising at propagation of high-frequency waves in a relaxing …

Y Sağlam Özkan, AR Seadawy… - Journal of Taibah …, 2021 - Taylor & Francis
In this study, based on the Hirota bilinear form, the exact analytic solutions of the (3+ 1)
dimensional Vakhnenko–Parkes equation with various physical properties were constructed …

A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation

VO Vakhnenko, EJ Parkes, AJ Morrison - Chaos, Solitons & Fractals, 2003 - Elsevier
A Bäcklund transformation both in bilinear and in ordinary form for the transformed
generalised Vakhnenko equation (GVE) is derived. It is shown that the equation has an …

Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko‐Parkes Equation

VO Vakhnenko, EJ Parkes - Advances in Mathematical Physics, 2016 - Wiley Online Library
A variety of methods for examining the properties and solutions of nonlinear evolution
equations are explored by using the Vakhnenko equation (VE) as an example. The VE …

Implementation of optical soliton behavior of the space–time conformable fractional Vakhnenko–Parkes equation and its modified model

SM Mabrouk, H Rezazadeh, H Ahmad… - Optical and Quantum …, 2024 - Springer
Fractional differential equations are being used to define numerous physical phenomena
instead of conventional ordinary or partial differential equations. The secret is to get more …

Internal solitons in the ocean

JR Apel, LA Ostrovsky, YA Stepanyants - The Journal of the Acoustical …, 1995 - pubs.aip.org
The well-known Garrett and Munk description of the internal wave spectrum synthesizes
many observations into a spectral model that reproduces the general features of the mid …

The calculation of multi-soliton solutions of the Vakhnenko equation by the inverse scattering method

VO Vakhnenko, EJ Parkes - Chaos, Solitons & Fractals, 2002 - Elsevier
A Bäcklund transformation both in bilinear form and in ordinary form for the transformed
Vakhnenko equation is derived. An inverse scattering problem is formulated. The inverse …

Internal solitons in laboratory experiments: Comparison with theoretical models

LA Ostrovsky, YA Stepanyants - Chaos: An Interdisciplinary Journal of …, 2005 - pubs.aip.org
Nonlinear internal solitary waves observed in laboratory experiments are discussed from the
standpoint of their relation to different soliton theories, from the classical integrable models …

[HTML][HTML] The N-loop soliton solutions for (2+ 1)-dimensional Vakhnenko equation

BQ Li, YL Ma, LP Mo, YY Fu - Computers & Mathematics with Applications, 2017 - Elsevier
Abstract A (2+ 1)-dimensional Vakhnenko equation is investigated, which describes high-
frequent wave propagations in relaxing medium. The N-loop soliton solutions for the …

On stationary solutions of the reduced Ostrovsky equation: Periodic waves, compactons and compound solitons

YA Stepanyants - Chaos, Solitons & Fractals, 2006 - Elsevier
Detailed analysis of solitary and periodic stationary solutions of the reduced Ostrovsky
equation is presented. The full Ostrovsky equation (ut+ c0ux+ αuux+ βuxxx) x= γu was …

Extraction of the gravitational potential and high‐frequency wave perturbation properties of nonlinear (3+ 1)‐dimensional Vakhnenko–Parkes equation via novel …

L Yan, H Mehmet Baskonus… - … Methods in the …, 2024 - Wiley Online Library
The (3+ 1)‐dimensional Vakhnenko–Parkes mathematical model has a wide range of
applications in science and engineering. In this paper, the model studied is investigated and …