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Asymptotics in shallow water waves

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  • In this paper we consider the initial value problem for a family of shallow water equations on the line $\mathbb{R}$ with various asymptotic conditions at infinity. In particular we construct solutions with prescribed asymptotic expansion as $x\to\pm\infty$ and prove their invariance with respect to the solution map.
    Mathematics Subject Classification: 35Q35, 37K65, 35Q53, 37K10.


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