Preprint A246/2003
Existence and Stability of Periodic Travelling-Wave Solutions of the Benjamin Equation
Jaime Angulo Pava | Alvarez Samaniego, Borys
Keywords: Existence | Stability | Periodic Travelling-Wave | Benjamin Equation | Hilbert transform.
Let $\H$ denote the periodic Hilbert transform and $l \in \mathbb{R}$. A proof of the existence and nonlinear stability of real even periodic travelling-wave solutions for the Benjamin Equation, $ u_t + u u_x + u_{xxx} +l \H u_{xx}=0$, is developed.