Results 21 to 30 of about 520 (49)

Efficient numerical scheme based on the method of lines for the shallow water equations

Journal of Ocean Engineering and Science, 2018
In this paper, a nonlinear shallow-water model of tsunami wave propagation at different points along a coastline of an ocean has been numerically simulated using method of lines.
Mohamed M. Mousa
doaj   +1 more source

On new computational and numerical solutions of the modified Zakharov–Kuznetsov equation arising in electrical engineering

Alexandria Engineering Journal, 2020
In this research, analytical and numerical solutions are studied of a two–dimensional discrete electrical lattice, which is mathematically represented by the modified Zakharov–Kuznetsov equation.
Choonkil Park, Mostafa M.A. Khater, Abdel-Haleem Abdel-Aty, Raghda A.M. Attia, Dianchen Lu   +4 more
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Solutions to the complex Korteweg-de Vries equation: Blow-up solutions and non-singular solutions [PDF]

, 2013
In the paper two kinds of solutions are derived for the complex Korteweg-de Vries equation, including blow-up solutions and non-singular solutions. We derive blow-up solutions from known 1-soliton solution and a double-pole solution.
Sun, Ying-ying, Yuan, Juan-ming, Zhang, Da-jun   +2 more
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Multi-solitons for nonlinear Klein–Gordon equations

Forum of Mathematics, Sigma, 2014
In this paper, we consider the existence of multi-soliton structures for the nonlinear Klein–Gordon (NLKG) equation in $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\
RAPHAËL CÔTE, CLAUDIO MUÑOZ
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Inverse Scattering Transform for the Camassa-Holm equation [PDF]

, 2006
An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are explicitly constructed in terms of the scattering data.
Adrian Constantin, Beals R, Bennewitz C, Birkhoff G, Camassa R, Constantin A, Constantin A, Constantin A, Gesztesy F, Hone A, Ivanov R I, Johnson R S, Lenells J, Lenells J, Li Y, Li Y, Novikov S P, Parker A, Parker A, Parker A, Rossen I Ivanov, Vladimir S Gerdjikov   +21 more
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On the central quadric ansatz: integrable models and Painleve reductions [PDF]

, 2012
It was observed by Tod and later by Dunajski and Tod that the Boyer-Finley (BF) and the dispersionless Kadomtsev-Petviashvili (dKP) equations possess solutions whose level surfaces are central quadrics in the space of independent variables (the so-called
A Zhang, B Huard, Calderbank D M J, Dryuma V, Dunajski M, E V Ferapontov, Ferapontov E V, Grundland A M, Huard B, Pavlov M V, Tod K P, Tsarev S P   +11 more
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Explicit solutions to the Korteweg-de Vries equation on the half line [PDF]

, 2006
Certain explicit solutions to the Korteweg-de Vries equation in the first quadrant of the $xt$-plane are presented. Such solutions involve algebraic combinations of truly elementary functions, and their initial values correspond to rational reflection ...
Ablowitz M J, Ablowitz M J, Aktosun T, Aktosun T, Bart H, Carl B, Chadan K, Coddington E A, Cornelis van der Mee, Deift P, Faddeev L D, Hirota R, Huang N N, Konopel'chenko B G, Marchenko V A, Marchenko V A, Matveev V B, Treibich A, Tuncay Aktosun   +18 more
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Generalized KdV Equation for Fluid Dynamics and Quantum Algebras

, 1996
We generalize the non-linear one-dimensional equation of a fluid layer for any depth and length as an infinite order differential equation for the steady waves.
A. A. Mohammad, A. C. Scott, A. J. Macfarlane, A. Ludu, A. Ludu, A. Ludu, A. Marshakov, C. Rebbi, D. J. Korteweg, G. B. Witham, G. L. Lamb, L. Branges de, L. Landau, M. Jimbo, R. A. Ionescu, R. M. Miura, S. Novikov, S. V. Vladimirov, V. Petviashvili, W. Greiner   +19 more
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Hirota derivatives and representation theory [PDF]

, 2001
It is shown that the Hirota derivative can be used to construct the plethysm for tensor products of representations of {sl}_2(k)
Athorne, C.
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Functional representation of the negative AKNS hierarchy [PDF]

, 2012
This paper is devoted to the negative flows of the AKNS hierarchy. The main result of this work is the functional representation of the extended AKNS hierarchy, composed of both positive (classical) and negative flows.
Vekslerchik, V. E.
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