Asymptotics for the modified witham equation
Nakao Hayashi, Pavel Ivanovich Naumkin, Isahi Sánchez-Suárez · Communications on Pure & Applied Analysis · 2018
We consider the modified Witham equation${{\partial }_{t}}v+{{\partial }_{x}}\sqrt{{{a}^{2}}-\partial _{x}^{2}v}={{\partial }_{x}}\left( {{v}^{3}} \right),\ \ \left( t,x \right)\in \mathbb{R}\times \mathbb{R},$where $\sqrt{a^{2}-\partial _{x}^{2}}$ means the dispersion relation which correspond to nonlinear Kelvin and continental-shelf waves. We develop the factorization technique to study the large time asymptotics of solutions.