Hamiltonian symmetry classification, integrals, and exact solutions of a generalized Ermakov system

2020 ◽  
Author(s):  
R. Naz ◽  
F. M. Mahomed
Keyword(s):  
Exact Solutions ◽  
Symmetry Classification

Symmetry classification and exact solutions of the Kramers equation

1998 ◽  
Vol 39 (6) ◽  
pp. 3505-3510 ◽  
Author(s):  
Stanislav Spichak ◽  
Valerii Stognii
Keyword(s):  
Exact Solutions ◽  
Symmetry Classification ◽  
Kramers Equation

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

2020 ◽  
Vol 11 (1) ◽  
pp. 93-100
Author(s):  
Vina Apriliani ◽  
Ikhsan Maulidi ◽  
Budi Azhari
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Internal Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Innovative Methods ◽  
De Vries

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations. 

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