Generalized function treatment of the Alfvén-gravity wave problem.
Debnath, L., Vajravelu, K. (1983)
International Journal of Mathematics and Mathematical Sciences
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Debnath, L., Vajravelu, K. (1983)
International Journal of Mathematics and Mathematical Sciences
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Karjanto, N., Tiong, K.M. (2011)
Journal of Applied Mathematics
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Samer Israwi (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We study here the water waves problem for uneven bottoms in a highly nonlinear regime where the small amplitude assumption of the Korteweg-de Vries (KdV) equation is enforced. It is known that, for such regimes, a generalization of the KdV equation (somehow linked to the Camassa-Holm equation) can be derived and justified [Constantin and Lannes, (2009) 165–186] when the bottom is flat. We generalize here this result with a new class of equations taking into account variable bottom...
Franco, Sebastião Romero, Farina, Leandro
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A Fourier approximation method is used for modeling and simulation of fully nonlinear steady waves. The set of resulting nonlinear equations are solved by Newton's method. The shoaling of waves is simulated based on comparisons with experimental data. The wave heights and the angles of breaking are analysed until the limit of inadequacy of the numerical method. The results appear quite close to those criteria predicted by the theory of completely nonlinear surface waves and contribute...
Khader, M.M., Al-Bar, R.F. (2011)
Mathematical Problems in Engineering
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Manuel G. Velarde (1993)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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Nikolay Tzvetkov (2000)
Journées équations aux dérivées partielles
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We survey some recent results for the KP-II equation. We also give an idea for treating the “bad frequency interactions” of the bilinear estimates in the Fourier transform restriction spaces related to the KP-I equation.
Gera, Dinesh, Gautam, Mridul, Gangarao, Hota V.S. (1997)
International Journal of Mathematics and Mathematical Sciences
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Khan, Tara Prasad, Das, Mahadeb, Debnath, Lokenath (1979)
International Journal of Mathematics and Mathematical Sciences
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Bhatti, Zahid Rafiq, Durrani, Ijaz-Ur-Rahman (2001)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Igor Rodnianski (2005-2006)
Séminaire Bourbaki
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The paper provides a description of the wave map problem with a specific focus on the breakthrough work of T. Tao which showed that a wave map, a dynamic lorentzian analog of a harmonic map, from Minkowski space into a sphere with smooth initial data and a small critical Sobolev norm exists globally in time and remains smooth. When the dimension of the base Minkowski space is , the critical norm coincides with energy, the only manifestly conserved quantity in this (lagrangian) theory....