Stability of the NLS equation with viscosity effect.
Karjanto, N., Tiong, K.M. (2011)
Journal of Applied Mathematics
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Karjanto, N., Tiong, K.M. (2011)
Journal of Applied Mathematics
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Bogdan Przeradzki, Katarzyna Szymańska-Dębowska (2014)
Banach Center Publications
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The existence of a traveling wave with special properties to modified KdV and BKdV equations is proved. Nonlinear terms in the equations are defined by means of a function f of an unknown u satisfying some conditions.
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...
Gera, Dinesh, Gautam, Mridul, Gangarao, Hota V.S. (1997)
International Journal of Mathematics and Mathematical Sciences
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Khader, M.M., Al-Bar, R.F. (2011)
Mathematical Problems in Engineering
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Khalfallah, Mohammed (2007)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Anna Karczewska, Piotr Rozmej, Maciej Szczeciński, Bartosz Boguniewicz (2016)
International Journal of Applied Mathematics and Computer Science
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The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov-Galerkin method are used. It is shown that the FEM gives a reasonable description of the wave dynamics of soliton waves governed by extended KdV equations. Some new results for several cases of bottom shapes are presented. The numerical scheme presented here is suitable for taking into account stochastic...
Zayed, Elsayed M.E., Rahman, Hanan M.Abdel (2010)
Applied Mathematics E-Notes [electronic only]
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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...
Kovriguine, D.A., Maugin, G.A., Potapov, A.I. (2006)
Mathematical Problems in Engineering
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Osman, Frederick, Beech, Robert (2005)
Journal of Applied Mathematics and Decision Sciences
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