Abstract
For the Cauchy problem of the half-wave equation with -critical combined nonlinearities
we obtain the existence of traveling wave solution of the form
with
. If
, where
is a solution of the equation
we prove that the traveling wave is stable.
Acknowledgments
The authors are very grateful to the referee for his (her) valuable suggestions and helps for improving the representation of the paper. This work was supported by the NSFC under grant numbers 11971212, 11475073 and 11801519.
Disclosure statement
No potential conflict of interest was reported by the authors.