Open AccessClassification of two types of weak solutions to the Casimir equation for the Ito system
Author(s) -
John Haussermann,
Robert A. Van Gorder
Publication year - 2014
Publication title -
quarterly of applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.603
H-Index - 41
eISSN - 1552-4485
pISSN - 0033-569X
DOI - 10.1090/s0033-569x-2014-01347-x
Subject(s) - casimir effect , uniqueness , mathematics , nonlinear system , class (philosophy) , mathematical analysis , series (stratigraphy) , real line , power series , wave equation , physics , classical mechanics , computer science , quantum mechanics , paleontology , artificial intelligence , biology
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.