Application of the Volterra method to the solution of mixed wave equation problems

1972 ◽  
Vol 5 (1) ◽  
pp. 128-132
Author(s):  
V. N. Mikhailov ◽  
A. I. Utkin
Keyword(s):  
Wave Equation ◽  
Mixed Wave ◽  
Volterra Method

scholarly journals Internal boundary value problems with displacement for the mixed-wave equation

2021 ◽  
pp. 8-14
Author(s):  
Ж.А. Балкизов ◽  
В.А. Водахова
Keyword(s):  
Wave Equation ◽  
Boundary Value Problems ◽  
Explicit Form ◽  
Boundary Value ◽  
Goursat Problem ◽  
Internal Boundary ◽  
Boundary Displacement ◽  
Mixed Wave

В работе исследованы краевые задачи с внутреннекраевым смещением для модельного смешанно-волнового уравнения, которые являются обобщениями задачи Гурса и задач с данными на противоположных характеристиках. Показано, что при определенных условиях на заданные функции решение исследуемых задач существует, единственно и выписывается в явном виде. The paper investigates boundary value problems with an internal boundary displacement for a model mixed-wave equation, which are generalizations of the Goursat problem and problems with data on opposite characteristics. It is shown that, under certain conditions for given functions, the solution to the problems under study exists, is unique, and is written out in an explicit form.

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. 

DeWitt geometry and the wave equation in hyper-volume

2020 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Wave Equation

DeWitt geometry and the wave equation in hyper-volume

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