Related papers: On The Stability of the Compacton Solutions
We derive a general theorem relating the energy, momentum and velocity of any solitary wave solution of the generalized KdV equation which enables us to relate the amplitude, width, and momentum to the velocity of these solutions. We obtain…
We initiate the study of stability of solutions of the 2D inviscid incompressible porous medium equation (IPM). We begin by classifying all stationary solutions of the inviscid IPM under mild conditions. We then prove some linear stability…
We prove nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as $x\to\infty$. We find that the amplitude of the line soliton converges to that of the…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
This brief gives a set of unified Lyapunov stability conditions to guarantee the predefined-time/finite-time stability of a dynamical systems. The derived Lyapunov theorem for autonomous systems establishes equivalence with existing…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
Families of analytical solutions are found for symmetric and antisymmetric solitons in the dual-core system with the Kerr nonlinearity and PT-balanced gain and loss. The crucial issue is stability of the solitons. A stability region is…
Stability of spatially inhomogeneous solutions to the Vlasov equation is investigated for the Hamiltonian mean-field model to provide the spectral stability criterion and the formal stability criterion in the form of necessary and…
The stability properties of a class of dissipative quantum mechanical systems are investigated. The nonlinear stability and asymptotic stability of stationary states (with zero and nonzero dissipation respectively) is investigated by…
We present a unified approach for qualitative and quantitative analysis of stability and instability dynamics of positive bright solitons in multi-dimensional focusing nonlinear media with a potential (lattice), which can be periodic,…
Dispersion-managed solitons are reviewed within a Gaussian variational approximation and an integral evolution model. In the normal regime of the dispersion map (when the averaged path dispersion is negative), there are two solitons of…
Linear stability of multi-vector-soliton bound states in the coupled nonlinear Schr\"odinger equations is analyzed using a new tail-matching method. Under the condition that individual vector solitons in the bound states are…
Many nonlinear dynamical systems can be written as Lure systems, which are described by a linear time-invariant system interconnected with a diagonal static sector-bounded nonlinearity. Sufficient conditions are derived for the global…
We consider the existence and stability of solitons in generalized galileons, scalar field theories with higher-derivative interactions but second-order equations of motion. It has previously been proven that no stable, static solitons…
The conditions under which stable evolution of two nonlinear interacting waves are derived within the context of nematic crystals. Two cases are considered: plane waves and solitons. In the first case, the modulation instability analysis…
We extend the definition of $n$-dimensional difference equations to complex order $\alpha\in \mathbb{C} $. We investigate the stability of linear systems defined by an $n$-dimensional matrix $A$ and derive conditions for the stability of…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
We explore stability regions for solitons in the nonlinear Schrodinger equation with a spatially confined region carrying a combination of self-focusing cubic and septimal terms, with a quintic one of either focusing or defocusing sign.…
The nonlinear Schr{\"o}dinger equation with derivative cubic nonlinearity admits a family of solitons, which are orbitally stable in the energy space. In this work, we prove the orbital stability of multi-solitons configurations in the…
This paper is concerned with stability analysis and synthesis for discrete-time linear systems with stochastic dynamics. Equivalence is first proved for three stability notions under some key assumptions on the randomness behind the…