Document Detail

Dynamical systems theory for nonlinear evolution equations.
MedLine Citation:
PMID:  21230205     Owner:  NLM     Status:  In-Process    
We observe that the fully nonlinear evolution equations of Rosenau and Hymann, often abbreviated as K(n,m) equations, can be reduced to Hamiltonian form only on a zero-energy hypersurface belonging to some potential function associated with the equations. We treat the resulting Hamiltonian equations by the dynamical systems theory and present a phase-space analysis of their stable points. The results of our study demonstrate that the equations can, in general, support both compacton and soliton solutions. For the K(2,2) and K(3,3) cases one type of solutions can be obtained from the other by continuously varying a parameter of the equations. This is not true for the K(3,2) equation for which the parameter can take only negative values. The K(2,3) equation does not have any stable point and, in the language of mechanics, represents a particle moving with constant acceleration.
Amitava Choudhuri; B Talukdar; Umapada Das
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Publication Detail:
Type:  Journal Article     Date:  2010-09-29
Journal Detail:
Title:  Physical review. E, Statistical, nonlinear, and soft matter physics     Volume:  82     ISSN:  1550-2376     ISO Abbreviation:  Phys Rev E Stat Nonlin Soft Matter Phys     Publication Date:  2010 Sep 
Date Detail:
Created Date:  2011-01-14     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  101136452     Medline TA:  Phys Rev E Stat Nonlin Soft Matter Phys     Country:  United States    
Other Details:
Languages:  eng     Pagination:  036609     Citation Subset:  -    
Department of Physics, Visva-Bharati, Santiniketan 731235, India.
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