Solitons of Whitham equation with resonance dispersion

Геворгян, Ашот Арутюнович; Kulagin, N. E.; Lerman, L. M.; Malkin, A.

doi:10.1016/j.chaos.2020.110550

Cited by 1 publication

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“…Smooth homoclinic orbits we call sometimes solitons and those with singularities cavitons. Here we follow our terminology in [13].…”

Section: Equation For Traveling Waves and Its Reductionmentioning

confidence: 99%

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Solitons and cavitons in a nonlocal Whitham equation

Kulagin,

Lerman,

Malkin

2020

Preprint

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Solitons and cavitons (localized solutions with singularities) for the nonlocal Whitham equations are studied. The equation of a fourth order with a parameter in front of fourth derivative for traveling waves is reduced to a reversible Hamiltonian system defined on a twosheeted four-dimensional space. When this parameter is small we get a slow-fast Hamiltonian system. Solutions of the system which stay on one sheet represent smooth solutions of the equation but those which perform transitions through the branching plane represent solutions with jumps. They correspond to solutions with singularities -breaks of the first and third derivatives but continuous even derivatives. The system has two types of equilibria on different sheets, they can of saddle-center or saddle-foci. Using analytic and numerical methods we found many types of homoclinic (and periodic as well) orbits to these equilibria both with a monotone asymptotics and oscillating ones. They correspond to solitons and cavitons of the initial equation. When we deal with homoclinic orbits to a saddle-center the values of the second parameter (physical wave speed) is discrete but for the case of a saddle-center it is continuous. The presence of majority such solutions displays the very complicated dynamics of the system.

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“…Smooth homoclinic orbits we call sometimes solitons and those with singularities cavitons. Here we follow our terminology in [13].…”

Section: Equation For Traveling Waves and Its Reductionmentioning

confidence: 99%

“…With small D 2 it is also applicable to the waves in a medium with internal oscillators [12]. A tentative analysis of some peculiarities of solitons to that equation has been performed in a short communication [13].…”

Section: Introductionmentioning

confidence: 99%

Solitons and cavitons in a nonlocal Whitham equation

Kulagin,

Lerman,

Malkin

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Solitons of Whitham equation with resonance dispersion

Cited by 1 publication

References 11 publications

Solitons and cavitons in a nonlocal Whitham equation

Solitons and cavitons in a nonlocal Whitham equation

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