Continuous Dependence for the Damped Nonlinear Hyperbolic Equation

Asymptotic Behavior of Solutions to the Damped Nonlinear Hyperbolic Equation

(x 1 , . . . , x n ) ∈ Rn and t > 0, k 1 > 0 and k 2 > 0 are constants. The nonlinear termf(u) = O(u1+θ) and θ is a positive integer. Equation (1) is a model in variational form for the neoHookean elastomer rod and describes the motion of a neoHookean elastomer rod with internal damping; for more detailed physical background, we refer to [1]. In [1], the authors have studied a general class of ...

Stability of Travelling Waves for a Damped Hyperbolic Equation

We consider a nonlinear damped hyperbolic equation in R, 1 ≤ n ≤ 4, depending on a positive parameter ǫ. If we set ǫ = 0, this equation reduces to the well-known Kolmogorov-Petrovski-Piskunov equation. We remark that, after a change of variables, this hyperbolic equation has the same family of one-dimensional travelling waves as the KPP equation. Using various energy functionals, we show that, ...

Continuous Dependence for the Pseudoparabolic Equation

Asymptotic behaviour of strongly damped nonlinear hyperbolic equations

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Traveling Solitons in the Damped-driven Nonlinear Schrödinger Equation∗

The well-known effect of the linear damping on the moving nonlinear Schrödinger soliton (even when there is a supply of energy via the spatially homogeneous driving) is to quench its momentum to zero. Surprisingly, the zero momentum does not necessarily mean zero velocity. We show that two or more parametrically driven damped solitons can form a complex traveling with zero momentum at a nonzero...