A Rigidity Property for the Novikov Equation and the Asymptotic Stability of Peakons
Sign Up to like & getrecommendations! Published in 2021 at "Archive for Rational Mechanics and Analysis"
DOI: 10.1007/s00205-021-01658-z
Abstract: We consider weak solutions of the Novikov equation that lie in the energy space $$H^1$$ with non-negative momentum densities. We prove that a special family of such weak solutions, namely the peakons, is $$H^1$$ -asymptotically… read more here.
Keywords: novikov equation; rigidity property; property novikov; property ... See more keywords
The dispersionless Veselov–Novikov equation: symmetries, exact solutions, and conservation laws
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DOI: 10.1007/s13324-021-00563-8
Abstract: We study symmetries, invariant solutions, and conservation laws for the dispersionless Veselov–Novikov equation. The emphasis is placed on cases when the odes involved in description of the invariant solutions are integrable by quadratures. Then we… read more here.
Keywords: dispersionless veselov; novikov equation; solutions conservation; conservation ... See more keywords
An application of Pfaffians to multipeakons of the Novikov equation and the finite Toda lattice of BKP type
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DOI: 10.1016/j.aim.2018.09.023
Abstract: Abstract The Novikov equation is an integrable analogue of the Camassa–Holm equation with a cubic (rather than quadratic) nonlinear term. Both these equations support a special family of weak solutions called multipeakon solutions. In this… read more here.
Keywords: novikov equation; equation; toda lattice; finite toda ... See more keywords
Well-posedness and wave breaking of the degenerate Novikov equation
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DOI: 10.1016/j.jde.2017.05.027
Abstract: Abstract In this paper, we investigate the degenerate Novikov equation, which is proposed as a scaling limit of the Novikov equation, and is integrable since it admits bi-Hamiltonian structure and Lax-pair. Geometrically, it arises from… read more here.
Keywords: novikov equation; wave breaking; well posedness; equation ... See more keywords
Two-component generalizations of the Novikov equation
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DOI: 10.1080/14029251.2019.1613048
Abstract: Some two-component generalizations of the Novikov equation, except the Geng-Xue equation, are presented, as well as their Lax pairs and bi-Hamiltonian structures. Furthermore, we study the Hamiltonians of the Geng-Xue equation and discuss the homogeneous… read more here.
Keywords: generalizations novikov; novikov equation; component generalizations; equation ... See more keywords
Stability of Peakons and Periodic Peakons for the mCH-Novikov-CH Equation
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DOI: 10.3390/sym14081702
Abstract: Peakons and periodic peakons are two kinds of special symmetric traveling wave solutions, which have important applications in physics, optical fiber communication, and other fields. In this paper, we study the orbital stability of peakons… read more here.
Keywords: novikov equation; mch novikov; equation; peakons periodic ... See more keywords