Solitary wave families of a generalized microstructure PDE
Abbreviated Journal Title
Commun. Nonlinear Sci. Numer. Simul.
Generalized microstructure PDE; Solitary wave families; Reversible; systems; Homoclinic orbits; SMALL PERIODIC-ORBITS; REVERSIBLE-SYSTEMS; Mathematics, Applied; Mathematics, Interdisciplinary Applications; Mechanics; Physics, Fluids & Plasmas; Physics, Mathematical
Wave propagation in a generalized microstructure PDE, tinder the Mindlin relations, is considered. Limited analytic results exist for the occurrence of one family of solitary wave solutions of these equations. Since solitary wave solutions often play a central role in the long-time evolution of an initial disturbance, we consider such solutions here (via normal form approach) within the framework of reversible systems theory. Besides confirming the existence of the known family of solitary waves, we find a continuum of delocalized solitary waves (or homoclinics to small-amplitude periodic orbits). On isolated curves in the relevant parameter region, the delocalized waves reduce to genuine embedded solitons. The new family of solutions occur in regions of parameter space distinct from the known solitary wave solutions and are thus entirely new. Directions for future work are also mentioned. (C) 2008 Elsevier B.V. All rights reserved.
Communications in Nonlinear Science and Numerical Simulation
"Solitary wave families of a generalized microstructure PDE" (2009). Faculty Bibliography 2000s. 1787.