9 citations · 17 across the 9 of their papers we have counts for
10 papers
Asymptotic stability of fast solitary waves to the Benjamin Equation
May Abdallah, Mohamad Darwich, Luc Molinet
We prove the asymptotic stability of the high speed solitary waves to the Benjamin equation. This is done by establishing a Liouville property for the nonlinear evolution of the Be…
On the Uniqueness and Orbital Stability of Slow and Fast Solitary Wave Solutions of the Benjamin Equation
May Abdallah, Mohamad Darwich, Luc Molinet
This paper is devoted to the study of existence and properties of solitary waves of the Benjamin equation. The studied equation includes a parameter in front of the Benjamin-On…
On the stability of the solitary waves to the rotation Benjamin-Ono equation
Mohamad Darwich
In this paper, we study several aspects of solitary wave solutions of the rotation Benjamin-Ono equation. By solving a minimization problem on the line, we construct a family of ev…
On the generalized nonlinear Camassa-Holm equation
Mohamad Darwich, Samer Israwi, Raafat Talhouk
In this paper, a generalized nonlinear Camassa-Holm equation with time- and space-dependent coefficients is considered. We show that the control of the higher order dispersive term…
Global existence for the nonlinear fractional Schrödinger equation with fractional dissipation
Mohamad Darwich
We consider the initial value problem for the fractional nonlinear Schrödinger equation with a fractional dissipation. Global existence and scattering are proved depending on the o…
On the -critical nonlinear Schrodinger equation with an inhomogeneous damping term
Mohamad Darwich
We consider the -critical nonlinear Schrodinger equation with an inhomogeneous damping term. We prove that there exists an initial data such that the corresponding solution is…
Some remarks on the nonlinear Schrödinger equation with fractional dissipation
Mohamad Darwich, Luc Molinet
We consider the Cauchy problem for the -critical nonlinear Schrödinger equation with a fractional dissipation. According to the order of the fractional dissipation, we prove t…
On the -critical nonlinear Schrödinger Equation with a nonlinear damping
Mohamad Darwich
We consider the Cauchy problem for the -critical nonlinear Schrödinger equation with a nonlinear damping. According to the power of the damping term, we prove the global exi…
On the well-posedness for Kadomtsev-Petviashvili-Burgers I equation
Mohamad Darwich
We prove local and global well-posedness in , , for the Cauchy problem associated with the Kadomotsev-Petviashvili-Burgers-I equation (KPBI) by w…
Blowup for the Damped -Critical Nonlinear Schrödinger Equation
Mohamad Darwich
We consider the Cauchy problem for the -critical damped nonlinear Schrödinger equation. We prove existence and stability of finite time blowup dynamics with the log-log blow…