Wave equation with a stochastic measure

2017 ◽  
Vol 94 ◽  
pp. 1-16 ◽  
Author(s):  
I. M. Bodnarchuk
Keyword(s):  
Wave Equation ◽  
Stochastic Measure

scholarly journals Asymptotics of the mild solution of awave equation in three-dimensional space driven by a general stochastic measure

2019 ◽  
pp. 12-17
Author(s):  
I. M. Bodnarchuk
Keyword(s):  
Cauchy Problem ◽  
Wave Equation ◽  
Mild Solution ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Absolute Value ◽  
Stochastic Measure ◽  
The Cauchy Problem ◽  
Three Dimensional Space ◽  
General Stochastic

We study the Cauchy problem for a wave equation in three-dimensional space driven by a general stochastic measure. Under some assumptions, we prove that the mild solution tends to zero almost surely as the absolute value of the spatial variable tends to infinity.

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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