scholarly journals EXACT SOLUTIONS FOR A BENJAMIN EQUATION WITH HIGHER-ORDER NONLINEARITY AND VARIABLE

2016 ◽  
Vol 110 (1) ◽  
Author(s):  
C.A. G\'omez S.
Keyword(s):  
Exact Solutions ◽  
Higher Order ◽  
Benjamin Equation

scholarly journals Double Reduction Analysis of Benjamin, DGH and Generalized DGH Equations

2020 ◽  
Vol Volume 14 ◽  
Keyword(s):  
Evolution Equation ◽  
Exact Solutions ◽  
Higher Order ◽  
Reduction Theory ◽  
Double Reduction ◽  
Linear Evolution ◽  
Holm Equation ◽  
Linear Evolution Equation ◽  
Non Linear ◽  
Benjamin Equation

The exact solutions of non-linear evolution equation, Benjamin equation, Dullin-Gottwald-Holm (DGH) equation and generalized Dullin-Gottwald-Holm equation are established using the conserved vectors. The multiplier approach is applied to construct the conserved vectors for equations under consideration. For non-linear evolution equation three conserved vectors and for Benjamin equation four conserved vectors are obtained. The conserved vectors for DGH and generalized DGH equations were reported in [1]. The higher order multiplier is considered for DGH equation and a new conserved vector is found. The double reduction theory is utilized to obtain various exact solutions for Benjamin equation, DGH equation and generalized DGH equation.

scholarly journals Exact Solution of Modified Veselov–Novikov Equation and Some Applications in the Game Theory

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Damir Kurmanbayev
Keyword(s):  
Game Theory ◽  
Exact Solution ◽  
Exact Solutions ◽  
Geometric Interpretation ◽  
Higher Order ◽  
The Game Theory ◽  
Novikov Equation

A method of finding exact solutions of the modified Veselov–Novikov (mVN) equation is constructed by Moutard transformations, and a geometric interpretation of these transformations is obtained. An exact solution of the mVN equation is found on the example of a higher order Enneper surface, and given transformations are applied in the game theory via Kazakh proverbs in terms of trees.

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.

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