Meshless spectral method for solution of time-fractional coupled KdV equations

2019 ◽  
Vol 341 ◽  
pp. 321-334 ◽  
Author(s):  
Manzoor Hussain ◽  
Sirajul Haq ◽  
Abdul Ghafoor
Keyword(s):  
Spectral Method ◽  
Kdv Equations ◽  
Coupled Kdv Equations

scholarly journals Lie symmetry reductions and conservation laws for fractional order coupled KdV system

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hossein Jafari ◽  
Hong Guang Sun ◽  
Marzieh Azadi
Keyword(s):  
Conservation Laws ◽  
Fractional Order ◽  
Lie Symmetry ◽  
Theoretical Physics ◽  
Lie Symmetry Analysis ◽  
Kdv Equations ◽  
Ode System ◽  
Coupled Kdv Equations ◽  
Scientific Phenomena ◽  
New System

AbstractLie symmetry analysis is achieved on a new system of coupled KdV equations with fractional order, which arise in the analysis of several problems in theoretical physics and numerous scientific phenomena. We determine the reduced fractional ODE system corresponding to the governing factional PDE system.In addition, we develop the conservation laws for the system of fractional order coupled KdV equations.

Nonholonomic deformation of coupled and supersymmetric KdV equations and Euler–Poincaré–Suslov method

2015 ◽  
Vol 27 (04) ◽  
pp. 1550011 ◽  
Author(s):  
Partha Guha
Keyword(s):  
Kdv Equation ◽  
Infinite Dimensional ◽  
Kdv Equations ◽  
Finite Dimensional ◽  
Euler Top ◽  
Two Component ◽  
Finite Dimensional Case ◽  
Coupled Kdv Equations ◽  
The Right ◽  
Supersymmetric Kdv Equation

Recently, Kupershmidt [38] presented a Lie algebraic derivation of a new sixth-order wave equation, which was proposed by Karasu-Kalkani et al. [31]. In this paper, we demonstrate that Kupershmidt's method can be interpreted as an infinite-dimensional analogue of the Euler–Poincaré–Suslov (EPS) formulation. In a finite-dimensional case, we modify Kupershmidt's deformation of the Euler top equation to obtain the standard EPS construction on SO(3). We extend Kupershmidt's infinite-dimensional construction to construct a nonholonomic deformation of a wide class of coupled KdV equations, where all these equations follow from the Euler–Poincaré–Suslov flows of the right invariant L2 metric on the semidirect product group [Formula: see text], where Diff (S1) is the group of orientation preserving diffeomorphisms on a circle. We generalize our construction to the two-component Camassa–Holm equation. We also give a derivation of a nonholonomic deformation of the N = 1 supersymmetric KdV equation, dubbed as sKdV6 equation and this method can be interpreted as an infinite-dimensional supersymmetric analogue of the Euler–Poincaré–Suslov (EPS) method.

Painlevé Properties And Exact Solutions Of The Generalized Coupled Kdv Equations

2005 ◽  
Vol 60 (5) ◽  
pp. 313-320 ◽  
Author(s):  
Li-Jun Ye ◽  
Ji Lin
Keyword(s):  
Exact Solutions ◽  
Elliptic Function ◽  
Jacobi Elliptic Function ◽  
Negative Index ◽  
Kp Hierarchy ◽  
New Exact Solutions ◽  
Kdv Equations ◽  
Function Expansion ◽  
Coupled Kdv Equations ◽  
Jacobi Elliptic Function Expansion

The generalized coupled Korteweg-de Vries (GCKdV) equations as one case of the four-reduction of the Kadomtsev-Petviashvili (KP) hierarchy are studied in details. The Painlevé properties of the model are proved by using the standard Weiss-Tabor-Carnevale (WTC) method, invariant, and perturbative Painlev´e approaches. The meaning of the negative index k = −2 is shown, which is indistinguishable from the index k = −1. Using the standard and nonstandard Painlevé truncation methods and the Jacobi elliptic function expansion approach, some types of new exact solutions are obtained.

Exact solution of the Wick-type stochastic fractional coupled KdV equations

2014 ◽  
Vol 52 (10) ◽  
pp. 2482-2493 ◽  
Author(s):  
Jin Hyuk Choi ◽  
Hyunsoo Kim ◽  
Rathinasamy Sakthivel
Keyword(s):  
Exact Solution ◽  
Kdv Equations ◽  
Coupled Kdv Equations

scholarly journals On the local well-posedness for some systems of coupled KdV equations

2008 ◽  
Vol 69 (2) ◽  
pp. 692-715 ◽  
Author(s):  
Borys Alvarez-Samaniego ◽  
Xavier Carvajal
Keyword(s):  
Well Posedness ◽  
Kdv Equations ◽  
Coupled Kdv Equations
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