Conservative Difference Scheme of Solitary Wave Solutions of the Generalized Regularized Long-Wave Equation

Asma Rouatbi (), Manel Labidi () and Khaled Omrani ()
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Asma Rouatbi: Université de Sousse
Manel Labidi: Université de Sousse
Khaled Omrani: Université de Sousse

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 4, 1317-1342

Abstract: Abstract Conservative difference scheme for the nonlinear dispersive generalized regularized long-wave (GRLW) equation is proposed. Existence of its difference solutions has been shown. It is proved by the discrete energy method that the difference scheme is uniquely solvable, unconditionally stable and the convergence is of second-order in the maximum norm. The particular case known as the modified regularized long-wave (MRLW) equation is also discussed numerically in details. Furthemore, three invariants of motion are evaluated to determine the conservation properties of the problem. Interaction of two and three solitary waves are shown. Some numerical examples are given in order to validate the theoretical results.

Keywords: GRLW equation; difference scheme; conservation; existence; uniqueness; stability; convergence; MRLW equation; solitary waves; 65M06; 65M12; 65M15 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0468-7

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