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Article
Doubly periodic solutions and breathers of the Hirota equation: recurrence, cascading mechanism and spectral analysis
The Hirota equation is an extension of the nonlinear Schrödinger equation by incorporating third-order dispersion. Doubly periodic solutions for the Hirota equation are established in terms of theta and ellipt...
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Article
Employing the dynamics of poles in the complex plane to describe properties of rogue waves: case studies using the Boussinesq and complex modified Korteweg–de Vries equations
The dynamics and properties of rogue waves of two classical evolution equations are studied in terms of trajectories of the poles of the exact solutions, by analytically continuing the spatial variable to be c...
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Article
The effect of downstream resistance on flow diverter treatment of a cerebral aneurysm at a bifurcation: A joint computational-experimental study
Intracranial aneurysm can lead to hemorrhagic stroke upon rupture. Deployment of flow diverters can restrict the blood flow into aneurysm and mitigate the rupture risk. Computational fluid dynamics (CFD) and u...
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Article
Correlating Hemodynamic Changes and Occlusion Time after Flow Diverter Treatment of Bilateral Large Internal Carotid Artery Aneurysms
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Chapter
Modulational Instability and Rogue Waves in Shallow Water Models
It is now well known that the focussing nonlinear Schrödinger equation allows plane waves to be modulationally unstable, and at the same time supports breather solutions which are often invoked as models for r...
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Article
Changing forms and sudden smooth transitions of tsunami waves
In some tsunami waves travelling over the ocean, such as the one approaching the eastern coast of Japan in 2011, the sea surface of the ocean is depressed by a small metre-scale displacement over a multi-kilom...
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Article
Symmetric and antisymmetric nonlinear modes supported by dual local gain in lossy lattices
We introduce a discrete lossy system, into which a double “hot spot” (HS) is inserted, i.e., two mutually symmetric sites carrying linear gain and cubic nonlinearity. The system can be implemented as an array ...
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Article
Doubly periodic patterns of modulated hydrodynamic waves: Exact solutions of the Davey-Stewartson system
Exact doubly periodic standing wave patterns of the Davey-Stewartson (DS) equations are derived in terms of rational expressions of elliptic functions. In fluid mechanics, DS equations govern the evolution of ...
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Article
Solitons pinned to hot spots
We generalize a recently proposed model based on the cubic complex Ginzburg-Landau (CGL) equation, which gives rise to stable dissipative solitons supported by localized gain applied at a “hot spot” (HS), in ...
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Article
Spatial solitons supported by localized gain in nonlinear optical waveguides
We introduce a modification of the complex Ginzburg-Landau (CGL) equation with background linear loss and locally applied gain. The equation appertains to laser cavities based on planar waveguides, and also to...
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Article
A computational study on the biomechanical factors related to stent-graft models in the thoracic aorta
Endovascular aortic stent-graft is a new, minimally invasive procedure for treating thoracic aortic diseases, and has quickly evolved to be one of the standard treatments subject to anatomic constraints. This ...
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Article
Open AccessDoubly periodic waves of a discrete nonlinear Schrödinger system with saturable nonlinearity
A system of two discrete nonlinear Schrödinger equations of the Ablowitz-Ladik type with a saturable nonlinearity is shown to admit a doubly periodic wave, whose long wave limit is also derived. As a by-produc...
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Article
A novel class of model constitutive laws in nonlinear elasticity: Construction via Loewner theory
Using a solitonic connection, we show that the class of infinitesimal Bäcklund transformations originally introduced by Loewner in 1952 in a gasodynamic context results in physically interesting nonlinear mode...
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Article
Nonlinear excitations and “peakons” of a (2+1)-dimensional generalized Broer-Kaup system
Shallow water waves and a host of long wave phenomena are commonly investigated by various models of nonlinear evolution equations. Examples include the Korteweg–de Vries, the Camassa–Holm, and the Whitham–Bro...
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Article
A simple model for the two dimensional blood flow in the collapse of veins
Veins in the cardiovascular system may collapse if the internal pressure is less than the external pressure. Such collapse or buckling will have important consequence in terms of the rate of blood flow. Here a...
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Article
Validity of cause of death statements from relatives
In countries where death certificates are inaccessible for various reasons, cause of death statements made by relatives may gain greater importance. The validity of the cause of death of a deceased family memb...
