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Full-Text Articles in Physical Sciences and Mathematics
On The Coriolis Effect For Internal Ocean Waves, Rossen Ivanov
On The Coriolis Effect For Internal Ocean Waves, Rossen Ivanov
Conference papers
A derivation of the Ostrovsky equation for internal waves with methods of the Hamiltonian water wave dynamics is presented. The internal wave formed at a pycnocline or thermocline in the ocean is influenced by the Coriolis force of the Earth's rotation. The Ostrovsky equation arises in the long waves and small amplitude approximation and for certain geophysical scales of the physical variables.
On A Nonlocal Nonlinear Schrodinger Equation, Tihomir Valchev
On A Nonlocal Nonlinear Schrodinger Equation, Tihomir Valchev
Conference papers
We consider a nonlocal nonlinear Schr\"odinger equation recently proposed by Ablowitz and Musslimani as a theoretical model for wave propagation in {\it PT}-symmetric coupled wave-guides and photonic crystals. This new equation is integrable by means of inverse scattering method, i. e. it possesses a Lax pair, infinite number of integrals of motion and exact solutions. We aim to describe here some of the basic properties of the nonlocal Schr\"odinger equation and its scattering operator. In doing this we shall make use of methods alternative to those applied by Ablowitz and Musslimani which seem to be better suited for treating possible …