Nonclassical Symmetries and the Singular Manifold Method: Theory and Six Examples

1995 ◽  
Vol 95 (1) ◽  
pp. 73-113 ◽  
Author(s):  
P. G. Estévez ◽  
P. R. Gordoa
Keyword(s):  
Singular Manifold ◽  
Nonclassical Symmetries ◽  
Singular Manifold Method

Localized Coherent Structures and their Interactions for the Melnikov Equation

2006 ◽  
Vol 61 (5-6) ◽  
pp. 253-257 ◽  
Author(s):  
Yan-Ze Peng
Keyword(s):  
Coherent Structures ◽  
Singular Manifold ◽  
The Creation ◽  
Singular Manifold Method

A general functional separation solution, containing two arbitrary functions, is first obtained for the Melnikov equation by means of the singular manifold method. Some novel localized coherent structures are given by appropriately choosing these arbitrary functions, whose interaction properties are numerically studied. The creation and annihilation phenomenon of dromion structure is reported. PACS numbers: 05.45.Yv, 02.30.Ik, 02.30.Jr

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