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Nonlinear Dispersive Systems: Theory and Examples
Author(s) -
Howes F. A.
Publication year - 1983
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm198369175
Subject(s) - nonlinear system , mathematics , scalar (mathematics) , boundary value problem , mathematical analysis , third order , partial differential equation , differential equation , physics , philosophy , geometry , theology , quantum mechanics
Some recent results in the asymptotic theory of differential equations are applied to certain third‐order scalar and vector boundary‐value problems that model various nonlinear physicochemical and dispersive wave phenomena. The key to our approach is the reduction of the third‐order problems to asymptotically equivalent second‐order ones which are more amenable to analysis. Many examples are discussed, including the problem of solitary‐wave solutions of generalized Korteweg‐de Vries equations and coupled systems of such equations.