The paper provides a direct proof the uniqueness of solutions to the Camassa-Holm equation, based on characteristics. Given a conservative solution u = u(t, x), an equation is introduced which singles out a unique characteristic curve through each initial point. By studying the evolution of the quantities u and v = 2 arctan ux along each characteristic, it is proved that the Cauchy problem with general initial data u0∈ H1(R) has a unique solution, globally in time.
|Original language||English (US)|
|Number of pages||18|
|Journal||Discrete and Continuous Dynamical Systems- Series A|
|State||Published - Jan 1 2015|
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics