Stability of solitary waves in the generalized Benjamin-Ono equation and its 2d extensions

December 9, 2021
We discuss solitary wave solutions in the generalized Benjamin-Ono equation, including the critical and supercritical cases. We then look at its higher-dimensional generalization in 2d, the Shrira equation, and its fractional generalization, the HBO (Higher-dimensional Benjamin-Ono) equation and examine the behavior of solutions in various cases as well as the stability of solitary waves.