Blowup of Solutions to the Two-Component Dullin–Gottwald–Holm System
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DOI: 10.1007/s40840-018-0672-3
Abstract: In this paper, we establish a new blow-up criterion for the two-component Dullin–Gottwald–Holm system. We show that strong solutions must blowup in finite time if the integral concerning initial momentum changes sign at some point… read more here.
Keywords: dullin gottwald; holm system; gottwald holm; component dullin ... See more keywords
“Local-in-space” Blowup Criterion for a Weakly Dissipative Dullin–Gottwald–Holm Equation
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DOI: 10.1007/s40840-020-01046-y
Abstract: We are concerned with the blowup phenomena of a dissipative Dullin–Gottwald–Holm equation which can describe unidirectional propagation of surface waves in a shallow water regime. A “local-in-space” blowup criterion is obtained by delicate analysis on… read more here.
Keywords: dullin gottwald; dissipative dullin; gottwald holm; holm equation ... See more keywords
The inverse scattering transform in the form of a Riemann-Hilbert problem for the Dullin-Gottwald-Holm equation
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DOI: 10.7494/opmath.2017.37.1.167
Abstract: The Cauchy problem for the Dullin-Gottwald-Holm (DGH) equation \[u_t-\alpha^2 u_{xxt}+2\omega u_x +3uu_x+\gamma u_{xxx}=\alpha^2 (2u_x u_{xx} + uu_{xxx})\] with zero boundary conditions (as \(|x|\to\infty\)) is treated by the Riemann-Hilbert approach to the inverse scattering transform method.… read more here.
Keywords: riemann hilbert; dullin gottwald; problem dullin; inverse scattering ... See more keywords