Numerical analysis of the regularized long-wave equation: Anelastic collision of solitary waves

1978 ◽  
Vol 46 (1) ◽  
pp. 179-188 ◽  
Author(s):  
A. R. Santarelli
Keyword(s):  
Wave Equation ◽  
Numerical Analysis ◽  
Solitary Waves ◽  
Long Wave ◽  
Regularized Long Wave Equation

scholarly journals Numerical investigation of nonlinear generalized regularized long wave equation via delta-shaped basis functions

2020 ◽  
Vol 10 (2) ◽  
pp. 244-258 ◽  
Author(s):  
Ömer Oruç
Keyword(s):  
Finite Element ◽  
Wave Equation ◽  
Finite Difference ◽  
Solitary Waves ◽  
Basis Functions ◽  
Long Wave ◽  
Highly Nonlinear ◽  
Regularized Long Wave Equation ◽  
Waves Interaction ◽  
Grlw Equation

In this study we will investigate generalized regularized long wave (GRLW)equation numerically. The GRLW equation is a highly nonlinear partialdifferential equation. We use finite difference approach for timederivatives and linearize the nonlinear equation. Then for space discretizationwe use delta-shaped basis functions which are relatively few studiedbasis functions. By doing so we obtain a linear system of equationswhose solution is used for constructing numerical solution of theGRLW equation. To see efficiency of the proposed method four classictest problems namely the motion of a single solitary wave, interactionof two solitary waves, interaction of three solitary waves and Maxwellianinitial condition are solved. Further, invariants are calculated.The results of numerical simulations are compared with exact solutionsif available and with finite difference, finite element and some collocationmethods. The comparison indicates that the proposed method is favorableand gives accurate results.

scholarly journals On Galilean Invariant and Energy Preserving BBM-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 878
Author(s):  
Alexei Cheviakov ◽  
Denys Dutykh ◽  
Aidar Assylbekuly
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Numerical Simulations ◽  
Solitary Waves ◽  
Local Symmetry ◽  
Symmetry And Conservation Laws ◽  
Higher Order ◽  
Special Equation ◽  
Long Wave ◽  
Local Symmetries

We investigate a family of higher-order Benjamin–Bona–Mahony-type equations, which appeared in the course of study towards finding a Galilei-invariant, energy-preserving long wave equation. We perform local symmetry and conservation laws classification for this family of Partial Differential Equations (PDEs). The analysis reveals that this family includes a special equation which admits additional, higher-order local symmetries and conservation laws. We compute its solitary waves and simulate their collisions. The numerical simulations show that their collision is elastic, which is an indication of its S−integrability. This particular PDE turns out to be a rescaled version of the celebrated Camassa–Holm equation, which confirms its integrability.

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