Special exact soliton solutions for the K(2, 2) equation with non-zero constant pedestal

Special exact solutions of the K(2, 2) equation, u t + ( u 2) x + ( u 2) xxx = 0, are investigated by employing the qualitative theory of differential equations. Our procedure shows that the K(2, 2) equation either has loop soliton, cusped soliton and smooth soliton solutions when sitting on the non...

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Bibliographic Details
Published in:Applied mathematics and computation 2011-12, Vol.218 (8), p.4448-4457
Main Authors: Zhang, Lina, Chen, Aiyong, Tang, Jiade
Format: Article
Language:English
Subjects:
Compacton
Computation
Computer simulation
Cuspon
Differential equations
Exact sciences and technology
Exact solutions
Global analysis, analysis on manifolds
K(2, 2) equation
Loop soliton
Mathematical analysis
Mathematical models
Mathematics
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Ordinary differential equations
Partial differential equations
Sciences and techniques of general use
Single peak soliton
Smooth soliton
Solitons
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:Special exact solutions of the K(2, 2) equation, u t + ( u 2) x + ( u 2) xxx = 0, are investigated by employing the qualitative theory of differential equations. Our procedure shows that the K(2, 2) equation either has loop soliton, cusped soliton and smooth soliton solutions when sitting on the non-zero constant pedestal lim x→±∞ u = A ≠ 0, or possesses compacton solutions only when lim x→±∞ u = 0. Mathematical analysis and numerical simulations are provided for these soliton solutions of the K(2, 2) equation.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.10.025