Dynamical behaviors of solutions to nonlinear wave equations with vanishing local damping and Wentzell boundary conditions

2018 ◽  
Vol 69 (4) ◽  
Author(s):  
Chan Li ◽  
Jin Liang ◽  
Ti-Jun Xiao
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Nonlinear Wave Equations ◽  
Wentzell Boundary Conditions ◽  
Dynamical Behaviors

scholarly journals Exact Solution of Linear and Nonlinear Wave Equations by Double Laplace and Iterative Method

2019 ◽  
Vol 11 (5) ◽  
pp. 33
Author(s):  
Adesina K. Adio ◽  
Wumi S. Ajayi ◽  
Olabode O. Bamisile ◽  
Babatunde T. Akanbi
Keyword(s):  
Exact Solution ◽  
Iterative Method ◽  
Boundary Conditions ◽  
Laplace Transform ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Iteration Process ◽  
Nonlinear Wave Equations ◽  
Double Laplace Transform ◽  
Linear And Nonlinear

A coupling of double Laplace transform with Iterative method is used to solve linear and nonlinear wave equations subject to initial and boundary conditions. The iteration process leads to disappearance of noise terms and exact solution is obtained at first iteration. Through several examples, the convenience and efficiency of the method is demonstrated, showing its usefulness to overcome difficulties associated with some existing techniques.

BREAKING WAVE SOLUTIONS TO THE SECOND CLASS OF SINGULAR NONLINEAR TRAVELING WAVE EQUATIONS

2009 ◽  
Vol 19 (04) ◽  
pp. 1289-1306 ◽  
Author(s):  
JIBIN LI ◽  
XIAOHUA ZHAO ◽  
GUANRONG CHEN
Keyword(s):  
Dynamical Systems ◽  
Systems Theory ◽  
Nonlinear Wave ◽  
Traveling Wave ◽  
Wave Equations ◽  
Traveling Wave Solutions ◽  
Nonlinear Wave Equations ◽  
Breaking Wave ◽  
Dynamical Behaviors ◽  
Wave Solutions

The existence of breaking wave solutions of the second class of singular nonlinear wave equations is proved by methods from the dynamical systems theory. For the second class of singular nonlinear traveling wave equations, dynamical behaviors of the traveling wave solutions are completely classified and thoroughly discussed. Corresponding to some bounded orbits of the traveling systems, exact parametric representations of traveling wave solutions are derived within different parameter regions of the parameter space.

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