KdV Equation Model in Open Cylindrical Channel under Precession
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Nonlinear Mathematical Physics"
DOI: 10.1007/s44198-021-00007-8
Abstract: A new model for Korteweg and de-Vries equation (KdV) is derived. The system under study is an open channel consisting of two concentric cylinders, rotating about their vertical axis, which is tilted by slope $$\tau$$… read more here.
Keywords: open cylindrical; model open; kdv equation; equation model ... See more keywords
Degenerate Riemann theta functions, Fredholm and wronskian representations of the solutions to the KdV equation and the degenerate rational case
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Geometry and Physics"
DOI: 10.1016/j.geomphys.2020.104059
Abstract: Abstract We degenerate the finite gap solutions of the KdV equation from the general formulation given in terms of abelian functions when the gaps tend to points, to get solutions to the KdV equation given… read more here.
Keywords: theta functions; riemann theta; degenerate; solutions kdv ... See more keywords
Application scope of the reductive perturbation method to derive the KdV equation and CKdV equation in dusty plasma
Sign Up to like & getrecommendations! Published in 2023 at "Journal of Plasma Physics"
DOI: 10.1017/s0022377823000296
Abstract: The application scopes of two different reductive perturbation methods to derive the Korteweg–de Vries (KdV) equation and coupled KdV (CKdV) equation in two-temperature-ion dusty plasma are given by using the particle-in-cell (PIC) numerical method in… read more here.
Keywords: kdv; equation; reductive perturbation; kdv equation ... See more keywords
Nonplanar dust-acoustic waves and chaotic motions in Thomas Fermi dusty plasmas
Sign Up to like & getrecommendations! Published in 2018 at "Physics of Plasmas"
DOI: 10.1063/1.5016893
Abstract: The properties of linear and nonlinear nonplanar dust acoustic (DA) solitary waves and chaotic behavior are investigated in an unmagnetized Thomas Fermi dusty plasma, whose components are degenerate electrons, ions, and negatively charged inertial cold… read more here.
Keywords: geometry; dust; kdv equation; nonplanar dust ... See more keywords
A new integrable equation combining the modified KdV equation with the negative-order modified KdV equation: multiple soliton solutions and a variety of solitonic solutions
Sign Up to like & getrecommendations! Published in 2018 at "Waves in Random and Complex Media"
DOI: 10.1080/17455030.2017.1367440
Abstract: Abstract A new third-order integrable equation is constructed via combining the recursion operator of the modified KdV equation (MKdV) and its inverse recursion operator. The developed equation will be termed the modified KdV-negative order modified… read more here.
Keywords: integrable equation; modified kdv; equation; negative order ... See more keywords
Consistent Riccati expansion solvability, symmetries, and analytic solutions of a forced variable-coefficient extended Korteveg–de Vries equation in fluid dynamics of internal solitary waves
Sign Up to like & getrecommendations! Published in 2021 at "Chinese Physics B"
DOI: 10.1088/1674-1056/ac052a
Abstract: We study a forced variable-coefficient extended Korteweg–de Vries (KdV) equation in fluid dynamics with respect to internal solitary wave. Bäcklund transformations of the forced variable-coefficient extended KdV equation are demonstrated with the help of truncated… read more here.
Keywords: expansion; forced variable; variable coefficient; kdv equation ... See more keywords
A family of wave equations with some remarkable properties
Sign Up to like & getrecommendations! Published in 2018 at "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences"
DOI: 10.1098/rspa.2017.0763
Abstract: We consider a family of homogeneous nonlinear dispersive equations with two arbitrary parameters. Conservation laws are established from the point symmetries and imply that the whole family admits square integrable solutions. Recursion operators are found… read more here.
Keywords: family wave; family; equation; equations remarkable ... See more keywords
Complex Korteweg-de Vries equation: A deeper theory of shallow water waves.
Sign Up to like & getrecommendations! Published in 2021 at "Physical review. E"
DOI: 10.1103/physreve.103.022216
Abstract: Using Levi-Cività's theory of ideal fluids, we derive the complex Korteweg-de Vries (KdV) equation, describing the complex velocity of a shallow fluid up to first order. We use perturbation theory, and the long wave, slowly… read more here.
Keywords: water; theory; korteweg vries; kdv equation ... See more keywords
Fractional Dynamics and Analysis of Coupled Schrödinger-kdv Equation with Caputo-katugampola Type Memory
Sign Up to like & getrecommendations! Published in 2023 at "Journal of Computational and Nonlinear Dynamics"
DOI: 10.1115/1.4062391
Abstract: Fundamental purpose of the current research article is to analyze the behaviour of obtained results of time fractional nonlinear coupled Schrödinger-KdV equation,viaimplementing an effective analytical technique. In this work, Katugampola fractional derivative in Caputo type… read more here.
Keywords: coupled schr; dinger kdv; kdv equation; analysis ... See more keywords
Symmetry operators and exact solutions of a type of time-fractional Burgers–KdV equation
Sign Up to like & getrecommendations! Published in 2019 at "International Journal of Geometric Methods in Modern Physics"
DOI: 10.1142/s0219887819500324
Abstract: In this paper, group analysis of the fourth-order time-fractional Burgers–Korteweg–de Vries (KdV) equation is considered. Geometric vector fields of Lie point symmetries of the equation are investigated and the corresponding optimal system is found. Similarity… read more here.
Keywords: fractional burgers; equation; kdv equation; time fractional ... See more keywords
Construction of invariant solutions and conservation laws to the ( 2 + 1 ) $(2+1)$ -dimensional integrable coupling of the KdV equation
Sign Up to like & getrecommendations! Published in 2020 at "Boundary Value Problems"
DOI: 10.1186/s13661-020-01466-6
Abstract: Under investigation in this paper is the ( 2 + 1 ) $(2+1)$ -dimensional integrable coupling of the KdV equation which has applications in wave propagation on the surface of shallow water. Firstly, based on… read more here.
Keywords: coupling kdv; integrable coupling; dimensional integrable; conservation laws ... See more keywords