On the Cauchy problem for an integrable equation with peakon solutions (Q1409655)

The non-linear family of partial differential equations, \[ u_t+c_0u_x+\gamma u_{xxx}-\alpha^2 u_{txx}= (c_1u^2+c_2u_x^2+c_3uu_{xx})_x, \] contains the Korteweg-de Vries and the Camassa-Holm equations as particular cases. These two equations are considered ``integrable'', because for some boundary conditions they can be solved using linear methods. Another differential equation in this family with similar ``integrability'' properties is \[ u_t-u_{txx}+4uu_x= 3u_xu_{xx}+uu_{xxx}. \] The paper under review studies the Cauchy problem for the above equation.