Orbital stability of standing waves for semilinear wave equations with indefinite energy

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

Asymptotic stability of solitary waves in the Benney-Luke model of water waves

We study asymptotic stability of solitary wave solutions in the one-dimensional Benney-Luke equation, a formally valid approximation for describing two-way water wave propagation. For this equation, as for the full water wave problem, the classic variational method for proving orbital stability of solitary waves fails dramatically due to the fact that the second variation of the energy-momentum...

Solution of Wave Equations Near Seawalls by Finite Element Method

A 2D finite element model for the solution of wave equations is developed. The fluid is considered as incompressible and irrotational. This is a difficult mathematical problem to solve numerically as well as analytically because the condition of the dynamic boundary (Bernoulli’s equation) on the free surface is not fixed and varies with time. The finite element technique is applied to solve non...

On stability of standing waves of nonlinear Dirac equations

We consider the stability problem for standing waves of nonlinear Dirac models. Under a suitable definition of linear stability, and under some restriction on the spectrum, we prove at the same time orbital and asymptotic stability. We are not able to get the full result proved in [26] for the nonlinear Schrödinger equation, because of the strong indefiniteness of the energy.

On the Stability of Standing Waves of Klein-gordon Equations in a Semiclassical Regime

We investigate the orbital stability and instability of standing waves for two classes of Klein-Gordon equations in the semi-classical regime.