Solitary waves of the regularised long-wave equation

Gardner, L. R. T.; Gardner, G. A.

doi:10.1016/0021-9991(90)90047-5

Cited by 110 publications

(63 citation statements)

References 9 publications

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“…Finite difference methods were proposed based on both cubic and quintic splines in the papers [3,11]. Some variants of finite element and collocation methods were constructed for the RLW equation by using B-splines as weight and trial functions [6][7][8][9]. The use of cubic splines in numerical methods for finding solutions of PDEs leads to a matrix system which is tridiagonal, thus permitting the use of the Thomas algorithm.…”

Section: U X (At) = 0 U X (Bt) = 0 ---And Initial Conditionsmentioning

confidence: 99%

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Numerical integration of the RLW equation using cubic splines

2005

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Section: U X (At) = 0 U X (Bt) = 0 ---And Initial Conditionsmentioning

confidence: 99%

“…https://doi.org/10.1017/S1446181100009822 Dursun Irk, idris Dag and Abdiilkadir Dogan [8] Corresponding simulation for the solitary wave with smaller amplitude 0.09 was carried out for further verification of accuracy of the numerical methods. Invariants and error norms are also recorded at the same selected times in Table 2.…”

Section: J-oo J-oo J-oomentioning

confidence: 99%

Numerical integration of the RLW equation using cubic splines

2005

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“…The solitary wave interaction problem for the RLW equation has been studied numerically in several papers (see, for example, Refs. [13,15,16,30]) and, from this point of view, the present work can also be another starting-point in the treatment of this problem.…”

Section: Introductionmentioning

confidence: 99%

Error propagation in the numerical integration of solitary waves. The regularized long wave equation

Araújo

Durán

2001

Applied Numerical Mathematics

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We study the error propagation of time integrators of solitary wave solutions for the regularized long wave equation, u t + u x + 1 2 (u 2 ) x − u xxt = 0, by using a geometric interpretation of these waves as relative equilibria. We show that the error growth is linear for schemes that preserve invariant quantities of the problem and quadratic for 'nonconservative' methods. Numerical experiments are presented.

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“…We consider the general regularized long wave equation for long waves in shallow water as in [18][19][20][21][22]:…”

Section: The General Regularized Long Wave (Grlw) Equationmentioning

confidence: 99%

Sine-Function Method In The Soliton Solution Of Nonlinear Partial Differential Equations

Ráb

Akhter

2013

GANIT: J. Bangladesh Math. Soc.

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In this paper we establish a traveling wave solution for nonlinear partial differential equations using sine-function method. The method is used to obtain the exact solutions for three different types of nonlinear partial differential equations like general equal width wave equation (GEWE), general regularized long wave equation (GRLW), general Korteweg-de Vries equation(GKDV) which are the important soliton equations.

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Solitary waves of the regularised long-wave equation

Cited by 110 publications

References 9 publications

Numerical integration of the RLW equation using cubic splines

Numerical integration of the RLW equation using cubic splines

Error propagation in the numerical integration of solitary waves. The regularized long wave equation

Sine-Function Method In The Soliton Solution Of Nonlinear Partial Differential Equations

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