. . . . . . . . Manuscript . . . . . . . . Acknowledgements . . . . . . References . . . . . . . . . Figures Captions . . . . . . Figures . . . . . . . . . . ii 2 9 . . . 10 . . . 12 . . . 13 Spatiotemporal Chaos in the Nonlinear Three Wave Interaction Carson C. Chow, A. Bers and A.K. Ram Plasma Fusion Center and Research Laboratory of Electronics Massachusetts Institute of Technology Cambridge...

This paper explores the properties of nonlinear wave equations. The proof for the existence and uniqueness of solutions to the 1+1 dimensional linear wave equation with smooth data is given. The D’Alembert formula is then presented in its full generality for the nonlinear equation. Important properties like the domain of dependence and propagation of information are discussed and motivated. The...

where := −∂2 t +∆ and u[0] := (u, ut)|t=0. The equation is semi-linear if F is a function only of u, (i.e. F = F (u)), and quasi-linear if F is also a function of the derivatives of u (i.e. F = F (u,Du), where D := (∂t,∇)). The goal is to use energy methods to prove local well-posedness for quasilinear equations with data (f, g) ∈ Hs × Hs−1 for large enough s, and then to derive Strichartz esti...

The irregular wave disturbance attenuation problem for jacket-type offshore platforms involving the nonlinear characteristics is studied. The main contribution is that a digital-control-based approximation of optimal wave disturbances attenuation controller (AOWDAC) is proposed based on iteration control theory, which consists of a feedback item of offshore state, a feedforward item of wave for...

We report instability structures and nonlinear phenomena that arise when unstable and stable nonlinear wave fields are coupled nonlinearly. This interaction is modelled with an integrable system of cubic nonlinear Schrödinger (NLS) equations and plane wave data. The linearized analysis is straightforward, and robust to non-integrable perturbations. The coupled nonlinear Schrödinger (CNLS) model...

In this paper we study the Cauchy problem for the semilinear stochastic wave equation (@ 2

The analysis of nonlinear wave equations has experienced a dramatic growth in the last ten years or so. The key factor in this has been the transition from linear analysis, first to the study of bilinear and multilinear wave interactions, useful in the analysis of semilinear equations, and next to the study of nonlinear wave interactions, arising in fully nonlinear equations. The dispersion phe...

To minimize body motions, floating marine structures are often designed with natural frequencies far away from the spectrum of ocean waves. Such design considerations led to a class of deep draft caisson vessels (DDCV or spars). Even so, large resonant responses may still be generated by excitation from nonlinear interactions of waves with body motions. Past experiments indicated that a DDCV ex...