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We establish local exact control and local exponential stability of periodic solutions of fifth order Korteweg-de Vries type equations in H-s(& x1d54b;), s > 2. A dissipative term is incorporated into the control which, along with a propagation of regulari ...
Passive Kerr cavities driven by coherent laser fields display a rich landscape of nonlinear physics, including bistability, pattern formation, and localized dissipative structures (solitons). Their conceptual simplicity has for several decades offered an u ...
The extensive use of frequency-domain tools for analyzing and controlling linear systems have become indispensable for the control systems engineer. However, due to the increased performance demands on today's industrial systems, the effects of certain non ...
The extensive use of frequency-domain tools for analyzing and controlling linear systems have become indispensable for the control systems engineer. However, due to the increased performance demands on today's industrial systems, the effects of certain non ...
The extensive use of frequency-domain tools for analyzing and controlling linear systems have become indispensable for the control systems engineer. However, due to the increased performance demands on today's industrial systems, the effects of certain non ...
Elastic ribbons subjected to twist and stretch handle multiple morphological instabilities, amongst others, the longitudinally wrinkled and creased helicoids are investigated in the present paper as promising periodic nonlinear waveguides. Modeling the rib ...
Folding of the earth's crust, wrinkling of the skin, rippling of fruits, vegetables and leaves are all examples of natural structures that can have periodic buckling. Periodic buckling is also present in engineering structures such as compressed lattices, ...
Linear matrix equations, such as the Sylvester and Lyapunov equations, play an important role in various applications, including the stability analysis and dimensionality reduction of linear dynamical control systems and the solution of partial differentia ...
Periodic buckled beams possess a geometrically nonlinear, load-deformation relationship and intrinsic length scales such that stable, nonlinear waves are possible. Modeling buckled beams as a chain of masses and nonlinear springs which account for transver ...
In this note we combine a recent result by Geba [2] on the local wellposedness theory of systems of nonlinear wave equations with Q0 null-form structure with the classical Penrose compactification method to obtain a new small data global existence resul ...
