Algebraic operator method for the construction of solitary solutions to nonlinear differential equations

Solutions of the KdV equation are derived by the algebraic operator method based on generalized operators of differentiation. The algebraic operator method based on the generalized operator of differentiation is exploited for the derivation of analytic solutions to the KdV equation. The structure of...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation Vol. 18; no. 6; pp. 1374 - 1389
Main Authors: Navickas, Zenonas, Bikulciene, Liepa, Rahula, Maido, Ragulskis, Minvydas
Format: Journal Article
Language:English
Published: Elsevier B.V 01.06.2013
Subjects:
Algebra
Condition of existence
Derivation
Differentiation
Exact solutions
Generalized operator of differentiation
KdV equation
Mathematical analysis
Mathematical models
Nonlinearity
Operators
Solitary solution
KdV equation
Condition of existence
Generalized operator of differentiation
Solitary solution
ISSN:1007-5704, 1878-7274
Online Access:Get full text
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Summary:Solutions of the KdV equation are derived by the algebraic operator method based on generalized operators of differentiation. The algebraic operator method based on the generalized operator of differentiation is exploited for the derivation of analytic solutions to the KdV equation. The structure of solitary solutions and explicit conditions of existence of these solutions in the subspace of initial conditions are derived. It is shown that special solitary solutions exist only on a line in the parameter plane of initial and boundary conditions. This new theoretical result may lead to important findings in a variety of practical applications.
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ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2012.10.009