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- Solitons (2)
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- Benjamin-Ono equation (1)
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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Quotient-Transitivity And Cyclic Subgroup-Transitivity, Brendan Goldsmith, Ketao Gong
Quotient-Transitivity And Cyclic Subgroup-Transitivity, Brendan Goldsmith, Ketao Gong
Articles
We introduce two new notions of transitivity for Abelian 𝑝-groups based on isomorphism of quotients rather than the classical use of equality of height sequences associated with Abelian 𝑝-group theory. Unlike the classical theory where “most” groups are transitive, these new notions lead to much smaller classes, but even these classes are sufficiently large to be interesting.
On The Socles Of Fully Inert Subgroups Of Abelian P-Groups, Andrey R. Chekhlov, Peter V. Danchev, Brendan Goldsmith
On The Socles Of Fully Inert Subgroups Of Abelian P-Groups, Andrey R. Chekhlov, Peter V. Danchev, Brendan Goldsmith
Articles
We define the so-called fully inert socle-regular and weakly fully inert socle-regular Abelian p-groups and study them with respect to certain of their numerous interesting properties. For instance, we prove that in the case of groups of length ! these two group classes coincide but that in the case of groups of length ! + 1 they differ. Some structural and characterization results are also obtained. The work generalizes concepts which have been of interest recently in the theory of entropy in algebra and builds on recent investigations by the second and third named authors in Arch. Math. Basel (2009) …
Swirling Fluid Flow In Flexible, Expandable Elastic Tubes: Variational Approach, Reductions And Integrability, Rossen Ivanov, Vakhtang Putkaradze
Swirling Fluid Flow In Flexible, Expandable Elastic Tubes: Variational Approach, Reductions And Integrability, Rossen Ivanov, Vakhtang Putkaradze
Articles
Many engineering and physiological applications deal with situations when a fluid is moving in flexible tubes with elastic walls. In real-life applications like blood flow, a swirl in the fluid often plays an important role, presenting an additional complexity not described by previous theoretical models. We present a theory for the dynamics of the interaction between elastic tubes and swirling fluid flow. The equations are derived using a variational principle, with the incompressibility constraint of the fluid giving rise to a pressure-like term. In order to connect this work with the previous literature, we consider the case of inextensible and …
On The Intermediate Long Wave Propagation For Internal Waves In The Presence Of Currents, Joseph Cullen, Rossen Ivanov
On The Intermediate Long Wave Propagation For Internal Waves In The Presence Of Currents, Joseph Cullen, Rossen Ivanov
Articles
A model for the wave motion of an internal wave in the presence of current in the case of intermediate long wave approximation is studied. The lower layer is considerably deeper, with a higher density than the upper layer. The flat surface approximation is assumed. The fluids are incompressible and inviscid. The model equations are obtained from the Hamiltonian formulation of the dynamics in the presence of a depth-varying current. It is shown that an appropriate scaling leads to the integrable Intermediate Long Wave Equation (ILWE). Two limits of the ILWE leading to the integrable Benjamin-Ono and KdV equations are …
Camassa-Holm Cuspons, Solitons And Their Interactions Via The Dressing Method, Rossen Ivanov, Tony Lyons, Nigel Orr
Camassa-Holm Cuspons, Solitons And Their Interactions Via The Dressing Method, Rossen Ivanov, Tony Lyons, Nigel Orr
Articles
A dressing method is applied to a matrix Lax pair for the Camassa–Holm equation, thereby allowing for the construction of several global solutions of the system. In particular, solutions of system of soliton and cuspon type are constructed explicitly. The interactions between soliton and cuspon solutions of the system are investigated. The geometric aspects of the Camassa–Holm equation are re-examined in terms of quantities which can be explicitly constructed via the inverse scattering method.