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
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10.1512/iumj.2008.57.3333
10.1512/iumj.2008.57.3333
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Indiana Univ. Math. J. 57 (2008) 2377 - 2422
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