scholarly journals On the blow-up of solutions of a periodic nonlinear dispersive wave equation in compressible elastic rods

2003 ◽  
Vol 288 (1) ◽  
pp. 232-245 ◽  
Author(s):  
Zhaoyang Yin
Keyword(s):  
Wave Equation ◽  
Blow Up ◽  
Elastic Rods ◽  
Dispersive Wave ◽  
Nonlinear Dispersive Wave ◽  
Dispersive Wave Equation

scholarly journals On Blow-Up Structures for a Generalized Periodic Nonlinearly Dispersive Wave Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Ying Wang ◽  
Yunxi Guo ◽  
Fang Li
Keyword(s):  
Wave Equation ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Well Posedness ◽  
Dispersive Wave ◽  
Initial Value ◽  
Dispersive Wave Equation

The local well-posedness for a generalized periodic nonlinearly dispersive wave equation is established. Under suitable assumptions on initial valueu0, a precise blow-up scenario and several sufficient conditions about blow-up results to the equation are presented.

Folded Solitary Waves and Foldons in the (2+1)-Dimensional Long Dispersive Wave Equation

2003 ◽  
Vol 58 (5-6) ◽  
pp. 280-284
Author(s):  
J.-F. Zhang ◽  
Z.-M. Lu ◽  
Y.-L. Liu
Keyword(s):  
Wave Equation ◽  
Solitary Waves ◽  
Coherent Structures ◽  
Bäcklund Transformation ◽  
Dispersive Wave ◽  
Variable Separation ◽  
New Class ◽  
Localized Structures ◽  
Dispersive Wave Equation ◽  
03.65 Ge

By means of the Bäcklund transformation, a quite general variable separation solution of the (2+1)- dimensional long dispersive wave equation: λqt + qxx − 2q ∫ (qr)xdy = 0, λrt − rxx + 2r ∫ (qr)xdy= 0, is derived. In addition to some types of the usual localized structures such as dromion, lumps, ring soliton and oscillated dromion, breathers soliton, fractal-dromion, peakon, compacton, fractal and chaotic soliton structures can be constructed by selecting the arbitrary single valued functions appropriately, a new class of localized coherent structures, that is the folded solitary waves and foldons, in this system are found by selecting appropriate multi-valuded functions. These structures exhibit interesting novel features not found in one-dimensions. - PACS: 03.40.Kf., 02.30.Jr, 03.65.Ge.

A dispersive wave equation using nonlocal elasticity

2009 ◽  
Vol 337 (8) ◽  
pp. 591-595 ◽  
Author(s):  
Noël Challamel ◽  
Lalaonirina Rakotomanana ◽  
Loïc Le Marrec
Keyword(s):  
Wave Equation ◽  
Nonlocal Elasticity ◽  
Dispersive Wave ◽  
Dispersive Wave Equation
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