Nonlocal Symmetry Reductions, CTE Method and Exact Solutions for Higher-Order KdV Equation

2015 ◽  
Vol 63 (2) ◽  
pp. 125-128 ◽  
Author(s):  
Bo Ren ◽  
Xi-Zhong Liu ◽  
Ping Liu
Keyword(s):  
Exact Solutions ◽  
Kdv Equation ◽  
Higher Order ◽  
Nonlocal Symmetry ◽  
Symmetry Reductions

scholarly journals A Note on the Fractional Generalized Higher Order KdV Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Yongyi Gu
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Kdv Equation ◽  
Nonlinear Differential Equations ◽  
Mathematical Physics ◽  
Higher Order ◽  
Complex Method ◽  
Applied Method ◽  
De Vries

We obtain exact solutions to the fractional generalized higher order Korteweg-de Vries (KdV) equation using the complex method. It has showed that the applied method is very useful and is practically well suited for the nonlinear differential equations, those arising in mathematical physics.

scholarly journals Recursion Operator and Local and Nonlocal Symmetries of a New Modified KdV Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Qian Suping ◽  
Li Xin
Keyword(s):  
Exact Solutions ◽  
Kdv Equation ◽  
Symmetry Algebra ◽  
Original Model ◽  
Identity Transformation ◽  
Recursion Operator ◽  
Nonlocal Symmetries ◽  
Symmetry Reductions ◽  
Finite Dimensional ◽  
Modified Kdv Equation

The recursion operator of a new modified KdV equation and its inverse are explicitly given. Acting the recursion operator and its inverse on the trivial symmetry 0 related to the identity transformation, the infinitely many local and nonlocal symmetries are obtained. Using a closed finite dimensional symmetry algebra with both local and nonlocal symmetries of the original model, some symmetry reductions and exact solutions are found.

EXACT SOLUTIONS OF COUPLED KdV EQUATION DERIVED FROM THE COUPLED NLS EQUATION USING MULTIPLE SCALES METHOD

2011 ◽  
Vol 25 (29) ◽  
pp. 4021-4028
Author(s):  
FILIZ TAŞCAN ◽  
AHMET BEKIR
Keyword(s):  
Exact Solutions ◽  
Multiple Scales ◽  
Kdv Equation ◽  
Higher Order ◽  
Multiple Scales Method ◽  
Nonlinear Schrödinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Coupled Kdv Equation

In this paper, we have considered a generalized coupled higher-order nonlinear Schrödinger equations. We applied multiple scales method to coupled higher-order nonlinear Schrödinger equations to derive the coupled KdV equation. Then, the extended tanh method is applied to derived coupled KdV equation for exact solutions. The obtained results include solitary wave solutions.

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