The Cauchy Problem and the Stability of Solitary Waves of a Hyperelastic Dispersive Equation
نویسنده
چکیده
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) = φc(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.
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