Title
CLASSIFICATION OF TWO TYPES OF WEAK SOLUTIONS TO THE CASIMIR EQUATION FOR THE ITO SYSTEM
Abbreviated Journal Title
Q. Appl. Math.
Keywords
Casimir equation; Ito system; extended KdV equation; weak solutions; asymptotic series; Mathematics, Applied
Abstract
The existence and non-uniqueness of two classes of weak solutions to the Casimir equation for the Ito system is discussed. In particular, for (i) all possible travelling wave solutions and (ii) one vital class of self-similar solutions, all possible families of local power series solutions are found. We are then able to extend both types of solutions to the entire real line, obtaining separate classes of weak solutions to the Casimir equation. Such results constitute rare globally valid analytic solutions to a class of nonlinear wave equations. Closed-form asymptotic approximations are also given in each case, and these agree nicely with the numerical solutions available in the literature.
Journal Title
Quarterly of Applied Mathematics
Volume
72
Issue/Number
3
Publication Date
1-1-2014
Document Type
Article
Language
English
First Page
471
Last Page
490
WOS Identifier
ISSN
0033-569X
Recommended Citation
"CLASSIFICATION OF TWO TYPES OF WEAK SOLUTIONS TO THE CASIMIR EQUATION FOR THE ITO SYSTEM" (2014). Faculty Bibliography 2010s. 5425.
https://stars.library.ucf.edu/facultybib2010/5425
Comments
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