Minimax estimates for functionals of solutions of wave equations with time-periodic right-hand sides

1995 ◽  
Vol 77 (5) ◽  
pp. 3452-3457
Author(s):  
L. T. Adzhubey ◽  
O. G. Nakonechy ◽  
Yu. K. Pidlypenko
Keyword(s):  
Wave Equations ◽  
Solutions Of Wave Equations ◽  
Right Hand ◽  
Time Periodic

Path-integral solutions of wave equations with dissipation

1989 ◽  
Vol 62 (19) ◽  
pp. 2201-2204 ◽  
Author(s):  
Cecile DeWitt-Morette ◽  
See Kit Foong
Keyword(s):  
Path Integral ◽  
Wave Equations ◽  
Solutions Of Wave Equations ◽  
Integral Solutions

On the Parametrical Excitation of Nonlinearly Coupled Wave Equations

1995 ◽  
Author(s):  
A. H. P. van der Burgh ◽  
P. Kuznetsov ◽  
S. A. Vavilov
Keyword(s):  
Wave Equations ◽  
Operator Method ◽  
Dynamical Behaviour ◽  
Existence Theory ◽  
Rigorous Analysis ◽  
Coupled Wave Equations ◽  
Time Periodic Solutions ◽  
Transversal Vibrations ◽  
Time Periodic ◽  
Coupled Wave

Abstract In this paper a mathematical model for the study of the interaction of longitudinal and transversal vibrations in a stretched string is presented. The study implies an existence theory for time periodic transversal vibrations generated by a horizontal excitation of one of the end-points of the string. The conditions for the existence of this parametrically excited time periodic vibrations are evaluated in a practical application. The innovative character of the results obtained concern the application of an operator method to a system of nonlinearly coupled wave equations modeling the dynamical behaviour of a strectched string where unite elasticity is taken into account. It may be known that in the literature little attention has been paid to a rigorous analysis of time periodic solutions for systems of partial differential equations.

scholarly journals Travelling-Wave Solutions for Wave Equations with Two Exponential Nonlinearities

2018 ◽  
Vol 73 (10) ◽  
pp. 883-892
Author(s):  
Stefan C. Mancas ◽  
Haret C. Rosu ◽  
Maximino Pérez-Maldonado
Keyword(s):  
Dynamical Systems ◽  
Elliptic Equations ◽  
Hypergeometric Functions ◽  
Wave Equations ◽  
Constant Term ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Simple Method ◽  
Solutions Of Wave Equations ◽  
Wave Solutions

AbstractWe use a simple method that leads to the integrals involved in obtaining the travelling-wave solutions of wave equations with one and two exponential nonlinearities. When the constant term in the integrand is zero, implicit solutions in terms of hypergeometric functions are obtained, while when that term is nonzero, all the basic travelling-wave solutions of Liouville, Tzitzéica, and their variants, as as well sine/sinh-Gordon equations with important applications in the phenomenology of nonlinear physics and dynamical systems are found through a detailed study of the corresponding elliptic equations.

Some properties of the solutions of wave equations

1969 ◽  
Vol 21 (1) ◽  
pp. 138-161 ◽  
Author(s):  
L. J. F. Broer ◽  
L. A. Peletier
Keyword(s):  
Wave Equations ◽  
Solutions Of Wave Equations
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