scholarly journals Global solution to the Cauchy problem of the nonlinear double dispersive wave equation with strong damping

2009 ◽  
Vol 6 (4) ◽  
pp. 367-383 ◽  
Author(s):  
C. Song ◽  
Z. Yang
Keyword(s):  
Cauchy Problem ◽  
Wave Equation ◽  
Global Solution ◽  
Dispersive Wave ◽  
Strong Damping ◽  
The Cauchy Problem ◽  
Dispersive Wave Equation

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.

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