[1]
|
M. Abounouh, H. Al-Moatassime and S. Kaouri, Novel transparent boundary conditions for the regularized long wave equation, Int. J. Comput. Methods, 16 (2019), 1950021-1950047.
doi: 10.1142/S021987621950021X.
|
[2]
|
C. Besse, M. Ehrhardt and I. Lacroix-Violet, Discrete artificial boundary conditions for the linearized Korteweg-de Vries equation, Num. Meth. For. Partial Differential Equations, 32 (2016), 1455-1484.
doi: 10.1002/num.22058.
|
[3]
|
J. Boussinesq, Essai sur la théorie des eaux courantes, l'Acad. des Sci. Inst. Nat. France, 23 (1877). Available from: https://gallica.bnf.fr/ark:/12148/bpt6k56673076.texteImage.
|
[4]
|
D. S. Clark, Short proof of a discrete Gronwall inequality, Discrete Applied Mathematics, 16 (1987), 279-281.
doi: 10.1016/0166-218X(87)90064-3.
|
[5]
|
O. Goubet and J. Shen, On the dual Petrov-Galerkin formulation of the KdV equation in a finite interval, Adv. Differ. Equat., 12 (2007), 221-239.
|
[6]
|
R. Hirota, Exact solution of the Korteweg–de Vries equation for multiple collisions of solitons, Phys. Rev. Lett., 27 (1971), 1192-1196.
doi: 10.1103/PhysRevLett.27.1192.
|
[7]
|
W. Hereman, Shallow water waves and solitary waves, Encyclopedia of Complexity and Applied System Science, 480 (2009), 8112-8125.
doi: 10.1007/978-1-4614-1806-1_96.
|
[8]
|
B. Klaus, The Korteweg-de Vries Equation: History, Exact Solutions, and Graphical Representation, University of Osnabrück/Germany, 2000.
|
[9]
|
D. J. Korteweg and G. de Vries, On the change of form of long waves advancing in a rectangular canal and on a new type of long stationary waves, Philos Mag., 39 (1895), 422-443.
doi: 10.1080/14786449508620739.
|
[10]
|
N. A. Kudryashov and I. L. Chernyavskii, Nonlinear waves in fluid flow through a viscoelastic tube, Fluid. Dyn., 41 (2006), 49-62.
doi: 10.1007/s10697-006-0021-3.
|
[11]
|
H. G. Lee and J. Kim, A simple and robust boundary treatment for the forced Korteweg–de Vries equation, Commun. Nonlinear Sci. Numer. Simulat., 19 (2014), 2262-2271.
doi: 10.1016/j.cnsns.2013.12.019.
|
[12]
|
L. A. Ostrovsky and Y. A. Stepanyants, Do internal solitons exist in the ocean?, Rev. Geophys., 27 (1989), 293-310.
|
[13]
|
G. M. Phillips, Interpolation and Approximation by Polynomials, Canadian Mathematical Society, Springer, 2003.
doi: 10.1007/b97417.
|
[14]
|
J. S. Russell, Report of the committee on waves, Rep. Meet. Brit. Assoc. Adv. Sci., 7th Liverpool, 417, John Murray, London, 1837.
|
[15]
|
J. Shen, A new dual-Petrov-Galerkin method for third and higher odd-order differential equations: Application to the KdV equation, SIAM J. Numer. Anal., 41 (2003), 1595-1619.
doi: 10.1137/S0036142902410271.
|
[16]
|
R. S. Varga, Matrix iterative analysis, Springer Series in Computational Mathematics, SSCM, 27, Springer, Berlin, Heidelberg, 1962.
doi: 10.1007/978-3-642-05156-2.
|
[17]
|
H. Washimi and T. Taniuti, Propagation of ion-acoustic solitary waves of small amplitude, Phys. Rev. Lett., 966 (1966).
doi: 10.1103/PhysRevLett.17.996.
|
[18]
|
N. J. Zabusky and M. D. Kruskal, Interactions of solitons in a collisionless plasma and the recurrence of initial states, Phys. Rev. Lett., 15 (1965), 240-43.
|
[19]
|
C. Zheng, W. X. Wen and H. Han, Numerical solution to a linearized KdV equation on unbounded domain, Numer. Methods Partial Differ. Equations, 24 (2007), 383-399.
doi: 10.1002/num.20267.
|