1-Soliton solution and conservation laws for nonlinear wave equation in semiconductors

Biswas, Anjan; Kara, A. H.

doi:10.1016/j.amc.2010.09.054

Cited by 11 publications

(2 citation statements)

References 19 publications

(22 reference statements)

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“…Moreover, the equation corresponds to the generalized BBM equation when d = 2 , and to the KdV-BBM equation when d = 3; see [3,5,8,18].…”

Section: Introductionmentioning

confidence: 99%

Convergence analysis and numerical solution of the Benjamin-Bona-Mahony equation by Lie-Trotter splitting

2018

Turk J Math

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In this paper, an operator splitting method is used to analyze nonlinear Benjamin-Bona-Mahony-type equations. We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie-Trotter splitting is applied to the equation. The local error bounds are obtained by using the approach based on the differential theory of operators in a Banach space and the quadrature error estimates via Lie commutator bounds. The global error estimate is obtained via Lady Windermere's fan argument. Finally, to confirm the expected convergence order, numerical examples are studied.

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“…Moreover, the equation corresponds to the generalized BBM equation when d = 2 , and to the KdV-BBM equation when d = 3; see [3,5,8,18].…”

Section: Introductionmentioning

confidence: 99%

Convergence analysis and numerical solution of the Benjamin-Bona-Mahony equation by Lie-Trotter splitting

2018

Turk J Math

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“…Wave equation [18][19][20] is also one of hyperbolic partial differential equations [21][22][23]. The variational iteration method was employed in [24] for solving the one dimensional wave equation with mixed classical and integral boundary conditions.…”

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confidence: 99%

A shifted Jacobi collocation algorithm for wave type equations with non-local conservation conditions

2014

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Abstract:In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral approximation is investigated for the discretization of the spatial variable of such equations. It possesses spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is established for treating the non-local conservation conditions, and then the problem with its initial and non-local boundary conditions are reduced to a system of second-order ordinary differential equations in temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical examples with comparisons are given. The computational results demonstrate that the proposed algorithm is more accurate than finite difference method, method of lines and spline collocation approach. PACS (2008): 35K10, 65M70, 33C05Keywords: non-local boundary conditions • integral conservation condition • collocation method • shifted Jacobi-GaussLobatto quadrature • system of differential equations © Versita sp. z o.o.

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A Model Describing the Propagation of a Femtosecond Pulse in a Kerr Nonlinear Medium

2019

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1-Soliton solution and conservation laws for nonlinear wave equation in semiconductors

Cited by 11 publications

References 19 publications

Convergence analysis and numerical solution of the Benjamin-Bona-Mahony equation by Lie-Trotter splitting

Convergence analysis and numerical solution of the Benjamin-Bona-Mahony equation by Lie-Trotter splitting

A shifted Jacobi collocation algorithm for wave type equations with non-local conservation conditions

A Model Describing the Propagation of a Femtosecond Pulse in a Kerr Nonlinear Medium

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