NOTES AND CORRESPONDENCE Constituent Boussinesq Equations for Waves and Currents

Boussinesq Waves on Vertically Sheared Currents

Modeling Breaking Waves and Wave-induced Currents with Fully Nonlinear Boussinesq Equations

A Boussinesq-type wave model is developed to numerically investigate the breaking waves and wave-induced currents. All the nonlinear terms are retained in the governing equations to keep fully nonlinearity characteristics and it hence more suitable to describe breaking waves with strong nonlinearity in the nearshore region. The Boussinesq equations are firstly extended to incorporate wave break...

On a Class of Boussinesq Equations for Shallow Water Waves

The Euler’s equations describing the dynamics of capillarygravity water waves in two-dimensions are considered in the limits of small-amplitude and long-wavelength under appropriate boundary conditions. Using a double-series perturbation analysis, a general Boussinesq type of equation is derived involving the small-amplitude and longwavelength parameters. A recently introduced sixth-order Bouss...

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...

Strong instability of solitary waves for nonlinear Klein-Gordon equations and generalized Boussinesq equations

We study here instability problems of standing waves for the nonlinear Klein-Gordon equations and solitary waves for the generalized Boussinesq equations. It is shown that those special wave solutions may be strongly unstable by blowup in finite time, depending on the range of the wave’s frequency or the wave’s speed of propagation and on the nonlinearity.