Singular solutions to Protter's problem for (3+1)-D degenerate wave equation

2012 ◽  
Author(s):  
Aleksey Nikolov ◽  
Nedyu Popivanov
Keyword(s):  
Wave Equation ◽  
Singular Solutions ◽  
Degenerate Wave Equation

Abundant exact solutions to the strain wave equation in micro-structured solids

2021 ◽  
pp. 2150439
Author(s):  
Karmina K. Ali ◽  
R. Yilmazer ◽  
H. Bulut ◽  
Tolga Aktürk ◽  
M. S. Osman
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Exact Solutions ◽  
Rational Function ◽  
Physical Interpretation ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Singular Solutions ◽  
Strain Wave ◽  
Important Place

In this study, the strain wave equation in micro-structured solids which take an important place in solid physics is presented for consideration. The generalized exponential rational function method is used for this purpose which is one of the most powerful methods of constructing abundantly distinct, exact solutions of nonlinear partial differential equations. In micro-structured solids, wave propagation is based on the structure of the strain wave equation. As a consequence, we successfully received many different exact solutions, including non-topological solutions, periodic singular solutions, topological solutions, singular solutions, like periodic lump solutions. Furthermore, in order to better understand their physical interpretation, 2D, 3D, and counter plots are graphed for each of the solutions acquired.

scholarly journals Global existence of solutions to degenerate wave equations with dissipative terms

1999 ◽  
Vol 60 (1) ◽  
pp. 1-10
Author(s):  
Mohammed Aassila
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Asymptotic Behaviour ◽  
Wave Equations ◽  
Existence Of Solutions ◽  
Dissipative Term ◽  
Global Existence Of Solutions ◽  
Asymptotic Behaviour Of Solutions ◽  
Dissipative Terms ◽  
Degenerate Wave Equation

In this paper we prove the global existence and study the asymptotic behaviour of solutions to a degenerate wave equation with a nonlinear dissipative term.

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