Approximate Solution of Space-Time Fractional KdV Equation and Coupled KdV Equations

2020 ◽  
Vol 89 (1) ◽  
pp. 014002 ◽  
Author(s):  
Swapan Biswas ◽  
Uttam Ghosh ◽  
Susmita Sarkar ◽  
Shantanu Das
Keyword(s):  
Approximate Solution ◽  
Kdv Equation ◽  
Space Time ◽  
Kdv Equations ◽  
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.

Integrability of coupled KdV equations

Open Physics ◽  
2011 ◽  
Vol 9 (3) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Kdv Equation ◽  
Soliton Solutions ◽  
Resonance Phenomenon ◽  
Hirota’S Bilinear Method ◽  
Bilinear Method ◽  
Kdv Equations ◽  
Multiple Soliton Solutions ◽  
Coupled Kdv Equations ◽  
Singular Soliton ◽  
Multiple Singular Soliton Solutions

AbstractThe integrability of coupled KdV equations is examined. The simplified form of Hirota’s bilinear method is used to achieve this goal. Multiple-soliton solutions and multiple singular soliton solutions are formally derived for each coupled KdV equation. The resonance phenomenon of each model will be examined.

scholarly journals Iterative Solutions of Hirota Satsuma Coupled KDV and Modified Coupled KDV Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-18 ◽  
Author(s):  
Muhammad Jibran ◽  
Rashid Nawaz ◽  
Asfandyar Khan ◽  
Sajjad Afzal
Keyword(s):  
Approximate Solution ◽  
Iterative Method ◽  
Homotopy Analysis Method ◽  
Approximate Solutions ◽  
Analysis Method ◽  
Kdv Equations ◽  
Homotopy Analysis ◽  
Iterative Solutions ◽  
Coupled Kdv Equations ◽  
New Iterative Method

In this article the approximate solutions of nonlinear Hirota Satsuma coupled Korteweg De- Vries (KDV) and modified coupled KDV equations have been obtained by using reliable algorithm of New Iterative Method (NIM). The results obtained give higher accuracy than that of homotopy analysis method (HAM). The obtained solutions show that NIM is effective, simpler, easier, and explicit and gives a suitable way to control the convergence of the approximate solution.

Approximate Solution of Homogeneous and Nonhomogeneous 5αth-Order Space-Time Fractional KdV Equations

2020 ◽  
Vol 18 (01) ◽  
pp. 2050018
Author(s):  
Swapan Biswas ◽  
Uttam Ghosh
Keyword(s):  
Inverse Method ◽  
Fractional Derivatives ◽  
Differential Operators ◽  
Numerical Solutions ◽  
Vries Equation ◽  
Kdv Equation ◽  
Space Time ◽  
Analysis Method ◽  
Kdv Equations ◽  
Homotopy Analysis

In this paper, the semi-inverse method is applied to derive the Lagrangian of the [Formula: see text]th Korteweg de Vries equation (KdV). Then the time and space differential operators of the Lagrangian are replaced by corresponding fractional derivatives. The variation of the functional of this Lagrangian is devoted to lead the fractional Euler Lagrangian via Agrawal’s method, which gives the space-time fractional KdV equation. Jumarie derivative is used to obtain the space-time fractional KdV equations. The homotopy analysis method (HAM) is applied to solve the derived space-time fractional KdV equation. Then numerical solutions are compared with the known analytical solutions by tables and figures.

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.

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