Results 21 to 30 of about 8,881 (223)
Symmetry analysis and conservation laws of time fractional Airy type and other KdV type equations
AIMS Mathematics, 2023 We study the invariance properties of the fractional time version of the nonlinear class of equations $ u_{t}^{\alpha}-g(u)\; u_{x}-f(u)\; u_{xxx} = 0 $, where $ 0 < \alpha < 1 $ using some recently developed symmetry-based techniques.
Miguel Vivas-Cortez +5 more
doaj +1 more source
Some finite difference methods for solving linear fractional KdV equation
Frontiers in Applied Mathematics and Statistics, 2023 The time-fractional Korteweg de Vries equation can be viewed as a generalization of the classical KdV equation. The KdV equations can be applied in modeling tsunami propagation, coastal wave dynamics, and oceanic wave interactions.
Appanah Rao Appadu, Abey Sherif Kelil
doaj +1 more source
Modulation of Camassa--Holm equation and reciprocal transformations [PDF]
, 2005 We derive the modulation equations or Whitham equations for the Camassa--Holm (CH) equation. We show that the modulation equations are hyperbolic and admit bi-Hamiltonian structure.
Abenda, Simonetta, Grava, Tamara
core +2 more sources
Exact traveling wave solutions to higher order nonlinear equations
Journal of Ocean Engineering and Science, 2019 The present paper applies the new generalized (G′/G)-expansion method on three non-linear equations including the fifth-order Korteweg-de Vries equation, (3+1)-dimensional Modified KdV-Zakharov-Kuznetsov equation, and (3+1)-dimensional Jimbo-Miwa ...
Md Nur Alam, Xin Li
doaj +1 more source
On the calculation of finite-gap solutions of the KdV equation [PDF]
, 1999 A simple and general approach for calculating the elliptic finite-gap solutions of the Korteweg-de Vries (KdV) equation is proposed. Our approach is based on the use of the finite-gap equations and the general representation of these solutions in the ...
Bateman H. +10 more
core +2 more sources
Ain Shams Engineering Journal, 2018 In this paper, we present a numerical method proficient for solving a system of time–fractional partial differential equations. For this sake, we use spectral collection method based on shifted Chebyshev polynomials in space and finite difference method ...
Basim Albuohimad +2 more
doaj +1 more source
Korteweg-de Vries description of Helmholtz-Kerr dark solitons [PDF]
, 2006 A wide variety of different physical systems can be described by a relatively small set of universal equations. For example, small-amplitude nonlinear Schrödinger dark solitons can be described by a Korteweg-de Vries (KdV) equation.
Chamorro-Posada P +21 more
core +3 more sources
Optimally convergent hybridizable discontinuous Galerkin method for fifth-order Korteweg-de Vries type equations [PDF]
, 2017 We develop and analyze the first hybridizable discontinuous Galerkin (HDG) method for solving fifth-order Korteweg-de Vries (KdV) type equations. We show that the semi-discrete scheme is stable with proper choices of the stabilization functions in the ...
Chen, Yanlai, Dong, Bo, Jiang, Jiahua
core +2 more sources
Results in Physics, 2018 The aim of this paper is to study three space-time (3 + 1)-dimensional modified Korteweg-de Vries equations. Nonlinear space-time (3 + 1)-dimensional partial differential equations model many realistic problems in the fields of engineering, wave ...
Innocent Simbanefayi +1 more
doaj +1 more source