Related papers: Local Analysis of Nonlinear RMS Envelope Dynamics
We construct a directional spin wavelet framework on the sphere by generalising the scalar scale-discretised wavelet transform to signals of arbitrary spin. The resulting framework is the only wavelet framework defined natively on the…
This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and…
In this paper we prove the existence of a nontrivial non-negative radial solution for a quasilinear elliptic problem. Our aim is to approach the problem variationally by using the tools of critical points theory in an Orlicz-Sobolev space.…
A theory of higher rank multiresolution analysis is given in the setting of abelian multiscalings. This theory enables the construction, from a higher rank MRA, of finite wavelet sets whose multidilations have translates forming an…
Based on the known implicit solution for nonlinear plasma waves, an explicit solution was obtained in the form of decomposition into harmonics. The solution obtained exhibits a mechanism for steepening of nonlinear plasma wave as a result…
Multiple solutions are common in various non-convex problems arising from industrial and scientific computing. Nonetheless, understanding the nontrivial solutions' qualitative properties seems limited, partially due to the lack of efficient…
In the last fifteen years, a great progress has been made in the understanding of the nonlinear resonance dynamics of water waves. Notions of scale- and angle-resonances have been introduced, new type of energy cascade due to nonlinear…
Since the early works[1-4] on the so-called nondiffracting waves (called also Localized Waves), a great deal of results has been published on this important subject, from both the theoretical and the experimental point of view. Initially,…
For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order…
A mathematical model featuring the motion of a multilink wheeled vehicle is developed using a nonholonomic model. A detailed analysis of the inertial motion is made. Fixed points of the reduced system are identified, their stability is…
The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The…
Observations of distorted discs have highlighted the ubiquity of warps in a variety of astrophysical contexts. This has been complemented by theoretical efforts to understand the dynamics of warp evolution. Despite significant efforts to…
We use a multi-scale similarity analysis which gives specific relations between the velocity, amplitude and width of localized solutions of nonlinear differential equations, whose exact solutions are generally difficult to obtain.
The conceptual picture underlying resolvent analysis(RA) is that the nonlinear term in the Navier-Stokes(NS) equations provides an intrinsic forcing to the linear dynamics, a description inspired by control theory. The inverse of the linear…
We study the vibrational motion of membrane resonators upon strong drive in the strongly nonlinear regime. By imaging the vibrational state of rectangular siliconnitride membrane resonators and by analyzing the frequency response using…
In this paper, we discuss multiscale methods for nonlinear problems. The main idea of these approaches is to use local constraints and solve problems in oversampled regions for constructing macroscopic equations. These techniques are…
Volumetric maps are widely used in robotics due to their desirable properties in applications such as path planning, exploration, and manipulation. Constant advances in mapping technologies are needed to keep up with the improvements in…
A nonparametric procedure for robust regression estimation and for quantile regression is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each…
By application of a straightforward variational procedure we derive a simple, analytic upper bound on the ground-state energy eigenvalue of a semirelativistic Hamiltonian for (one or two) spinless particles which experience some…
A basis expansion with regularization methods is much appealing to the flexible or robust nonlinear regression models for data with complex structures. When the underlying function has inhomogeneous smoothness, it is well known that…