Related papers: Spectral Properties and Linear Stability of Self-S…
This paper concerns spectral stability of nonlinear waves in KdV-type evolution equations. The relevant eigenvalue problem is defined by the composition of an unbounded self-adjoint operator with a finite number of negative eigenvalues and…
In this paper, we consider the problem of mechanical wave scattering from a spatially finite system into an infinite surrounding environment. The goal is to illuminate why the scattering spectrum undergoes peaks and dips (resonances) at…
In this paper, the uniform stability of the inverse spectral problem is proved for the matrix Sturm-Liouville operator on a finite interval. Namely, we describe the sets of spectral data, on which the inverse spectral mapping is bounded…
We construct solitary wave solutions in a $1+1$ dimensional massless scalar ($\phi$) field theory with a specially chosen potential $V(\phi)$. The equation governing perturbations about this solitary wave has an effective potential which is…
We consider the existence and spectral stability of nonlinear discrete localized solutions representing light pulses propagating in a twisted multi-core optical fiber. By considering an even number, $N$, of waveguides, we derive asymptotic…
We present a model for spectral theory of families of selfadjoint operators, and their corresponding unitary one-parameter groups (acting in Hilbert space.) The models allow for a scale of complexity, indexed by the natural numbers…
The dynamics of metric perturbations is explored in the gravity theory with anomaly-induced quantum corrections. Our first purpose is to derive the equation for gravitational waves in this theory on the general homogeneous and isotropic…
The purpose of this paper is to establish a geometric scattering result for a conformally invariant nonlinear wave equation on an asymptotically simple spacetime. The scattering operator is obtained via trace operators at null infinities.…
This paper is devoted to studying impedance eigenvalues (that is, eigenvalues of a particular Dirichlet-to-Neumann map) for the time harmonic linear elastic wave problem, and their potential use as target-signatures for fluid-solid…
In this paper, we study the endpoint reversed Strichartz estimates along general time-like trajectories for wave equations in $\mathbb{R}^{3}$. We also discuss some applications of the reversed Strichartz estimates and the structure of wave…
We consider the Cauchy problem for wave maps u: \R times M \to N for Riemannian manifolds, (M, g) and (N, h). We prove global existence and uniqueness for initial data that is small in the critical Sobolev norm in the case (M, g) = (\R^4,…
In this article, a perturbation theory of the compressible Navier-Stokes equations in $\mathbb{R}^n$ $(n \geq 3)$ is studied to investigate decay estimate of solutions around a non-constant state. As a concrete problem, stability is…
The traveling wave with the peaked profile arises in the limit of the family of traveling waves with the smooth profiles. We study the linear and nonlinear stability of the peaked traveling wave by using a local model for shallow water…
In this paper, we explore the orbital stability of smooth solitary wave solutions to the modified Camassa-Holm equation with cubic nonlinearity. These solutions, which exist on a nonzero constant background $k$, are unique up to translation…
We address various issues concerning the Cauchy problem for the Zakharov-Rubenchik system (known as the Benney-Roskes system in water waves theory), which models the interaction of short and long waves in many physical situations. Motivated…
Following Smale, we study simple symmetric mechanical systems of $n$ point particles in the plane. In particular, we address the question of the linear and spectral stability properties of relative equilibria, which are special solutions of…
The inverse spectral problems are studied for the Sturm-Liouville operator on the star-shaped graph and for the matrix Sturm-Liouville operator with the boundary condition in the general self-adjoint form. We obtain necessary and sufficient…
In this paper, the regularity properties of Cauchy problem for linear and nonlinear nonlocal wave equations are studied.The equation involves a convolution integral operators with a general kernel operator functions whose Fourier transform…
We consider a spectral problem associated with steady water waves of extreme form on the free surface of a rotational flow. It is proved that the spectrum of this problem contains arbitrary large negative eigenvalues and they are simple.…
We present a rigorous functional analytic setting to study the radial wave equation in similarity coordinates. As an application we analyse linear stability of the fundamental self--similar solution of the wave equation with a focusing…