New exact solutions for the -dimensional Broer-Kaup-Kupershmidt equations.
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Song, Ming, Li, Shaoyong, Cao, Jun (2010)
Abstract and Applied Analysis
Khani, F., Samadi, F., Hamedi-Nezhad, S. (2009)
Mathematical Problems in Engineering
Zheng, Xuedong, Xia, Tiecheng, Zhang, Hongqing (2002)
Applied Mathematics E-Notes [electronic only]
Khalfallah, Mohammed (2007)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
Xia, Tiecheng, Li, Biao, Zhang, Hongqing (2001)
Applied Mathematics E-Notes [electronic only]
Borhanifar, A., Jafari, H., Karim, S.A. (2008)
The Journal of Nonlinear Sciences and its Applications
Joachim Krieger, Wilhelm Schlag (2009)
Journal of the European Mathematical Society
We consider the -critical focusing non-linear Schrödinger equation in -d. We demonstrate the existence of a large set of initial data close to the ground state soliton resulting in the pseudo-conformal type blow-up behavior. More specifically, we prove a version of a conjecture of Perelman, establishing the existence of a codimension one stable blow-up manifold in the measurable category.
J.M. Sanz-Serna, T. Ortega (1990/1991)
Numerische Mathematik
Xuan, Benjin (2003)
Revista Colombiana de Matemáticas
Yvan Martel, Frank Merle (2008)
Revista Matemática Complutense
Stéphane Labbé, Lionel Paumond (2004)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
The Benney-Luke equation (BL) is a model for the evolution of three-dimensional weakly nonlinear, long water waves of small amplitude. In this paper we propose a nearly conservative scheme for the numerical resolution of (BL). Moreover, it is known (Paumond, Differential Integral Equations 16 (2003) 1039–1064; Pego and Quintero, Physica D 132 (1999) 476–496) that (BL) is linked to the Kadomtsev-Petviashvili equation for almost one-dimensional waves propagating in one direction. We study here numerically...
Stéphane Labbé, Lionel Paumond (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
The Benney-Luke equation (BL) is a model for the evolution of three-dimensional weakly nonlinear, long water waves of small amplitude. In this paper we propose a nearly conservative scheme for the numerical resolution of (BL). Moreover, it is known (Paumond, Differential Integral Equations16 (2003) 1039–1064; Pego and Quintero, Physica D132 (1999) 476–496) that (BL) is linked to the Kadomtsev-Petviashvili equation for almost one-dimensional waves propagating in one direction. We study here numerically...
Laurent Di Menza (2009)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
In this paper, we present numerical methods for the determination of solitons, that consist in spatially localized stationary states of nonlinear scalar equations or coupled systems arising in nonlinear optics. We first use the well-known shooting method in order to find excited states (characterized by the number of nodes) for the classical nonlinear Schrödinger equation. Asymptotics can then be derived in the limits of either large are large nonlinear exponents . In a second part, we compute...
Laurent Di Menza (2008)
ESAIM: Mathematical Modelling and Numerical Analysis
In this paper, we present numerical methods for the determination of solitons, that consist in spatially localized stationary states of nonlinear scalar equations or coupled systems arising in nonlinear optics. We first use the well-known shooting method in order to find excited states (characterized by the number k of nodes) for the classical nonlinear Schrödinger equation. Asymptotics can then be derived in the limits of either large k are large nonlinear exponents σ. In a second part, we compute...
Al-Khaled, Kamel, Nusier, Ameina S. (2008)
Applied Mathematics E-Notes [electronic only]
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