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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
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
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
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...