scholarly journals Functionally separable solutions to nonlinear wave equations by group foliation method

2007 ◽  
Vol 330 (1) ◽  
pp. 298-311 ◽  
Author(s):  
Jiayi Hu ◽  
Changzheng Qu
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Nonlinear Wave Equations ◽  
Group Foliation

scholarly journals A uniqueness result for the Sine-Gordon breather

2021 ◽  
Vol 2 (2) ◽  
Author(s):  
Rainer Mandel
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Uniqueness Result ◽  
Nonlinear Wave Equations

AbstractIn this note we prove that the sine-Gordon breather is the only quasimonochromatic breather in the context of nonlinear wave equations in $$\mathbb {R}^N$$ R N .

scholarly journals Global existence and decay estimates for nonlinear wave equations with space-time dependent dissipative term

2015 ◽  
Vol 12 (02) ◽  
pp. 249-276
Author(s):  
Tomonari Watanabe
Keyword(s):  
Global Existence ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Space Time ◽  
Time Dependent ◽  
Nonlinear Wave Equations ◽  
Energy Estimates ◽  
Space Region ◽  
Decay Estimates ◽  
Dissipative Term

We study the global existence and the derivation of decay estimates for nonlinear wave equations with a space-time dependent dissipative term posed in an exterior domain. The linear dissipative effect may vanish in a compact space region and, moreover, the nonlinear terms need not be in a divergence form. In order to establish higher-order energy estimates, we introduce an argument based on a suitable rescaling. The proposed method is useful to control certain derivatives of the dissipation coefficient.

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