The Cauchy problem and the stability of solitary waves of a hyperelastic dispersive equation Robin Ming Chen 3576dispersive equationwell-posednesssolitary wavesstability We prove that the Cauchy problem for a certain sixth order hyperelastic dispersive equation is globally well-posed in a natural space. We also show that there exist solitary wave solutions $u(x,y,t) = phi_c(x - ct, y)$ that come from an associated variational problem. Such solitary waves are nonlinearly stable in the sense that if a solution is initially close to the set of such solitary waves, it remains close to the set for all time in the natural norm. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3333 10.1512/iumj.2008.57.3333 en Indiana Univ. Math. J. 57 (2008) 2377 - 2422 state-of-the-art mathematics http://iumj.org/access/