The Laplace residual power series method was introduced as an effective technique for finding exact and approximate solutions to various kinds of differential equations. In this context, we utilize the generate analytic partial Then, by resorting above-mentioned technique, derive certain different types linear nonlinear equations, including wave nonhomogeneous space telegraph water Klein–Gordon...

Tuned Liquid Dampers (TLD) are among passive control devices that have been used to suppress the vibration of structures in recent years. These structures must be adequately presentable as an equivalent single degree of freedom system with long fundamental period. The TLD, located at the top floors of the structure, can dissipate the external input energy into the system through the sloshing ef...

Tuned Liquid Dampers (TLD) are among passive control devices that have been used to suppress the vibration of structures in recent years. These structures must be adequately presentable as an equivalent single degree of freedom system with long fundamental period. The TLD, located at the top floors of the structure, can dissipate the external input energy into the system through the sloshing ef...

We study orbital stability of solitary waves of least energy for a nonlinear Kawahara type equation (Benney-Luke-Paumond) that models long water waves with small amplitude, from the analytic and numerical viewpoint. We use a second-order spectral scheme to approximate these solutions and illustrate their unstable behavior within a certain regime of wave velocity.

Abstract. A fully discrete a priori analysis of the finite element heterogenenous multiscale method (FE-HMM) introduced in [A. Abdulle, M. Grote, C. Stohrer, Multiscale Model. Simul. 2014] for the wave equation with highly oscillatory coefficients over long time is presented. A sharp a priori convergence rate for the numerical method is derived for long time intervals. The effective model over ...

Extended shallow water wave equations are derived, using the method of asymptotic expansions, from Euler (or wave) equations. These extended models valid one order beyond usual weakly nonlinear, long approximation, incorporating all appropriate dispersive and nonlinear terms. Specifically, first we derive Korteweg–de Vries (KdV) equation, then proceed with Benjamin–Bona–Mahony Camassa–Holm in (...

We study the approximate controllability of the stochastic Maxwell equations with an abstract approach and a constructive approach using a generalization of the Hilbert uniqueness method as proposed in Kim (2004, Approximate controllability of a stochastic wave equation. Appl. Math. Optim., 49, 81–98) for the stochastic wave equation.

The inverse water wave problem of bathymetry detection is the problem of deducing the bottom topography of the seabed from measurements of the water wave surface. In this paper, we present a fully nonlinear method to address this problem. The method starts from the Euler water wave equations for inviscid irrotational fluid flow, without any approximation. Given the water wave height and its fir...