SpecTraVVave
swMATH ID:  21398 
Software Authors:  Kalisch, Henrik; Moldabayev, Daulet; Verdier, Olivier 
Description:  A numerical study of nonlinear dispersive wave models with SpecTraVVave. In nonlinear dispersive evolution equations, the competing effects of nonlinearity and dispersion make a number of interesting phenomena possible. In the current work, the focus is on the numerical approximation of travelingwave solutions of such equations. We describe our efforts to write a dedicated mathsf{Python} code which is able to compute travelingwave solutions of nonlinear dispersive equations in a very general form. par The mathsf{SpecTraVVave} code uses a continuation method coupled with a spectral projection to compute approximations of steady symmetric solutions of this equation. The code is used in a number of situations to gain an understanding of travelingwave solutions. The first case is the Whitham equation, where numerical evidence points to the conclusion that the main bifurcation branch features three distinct points of interest, namely a turning point, a point of stability inversion, and a terminal point which corresponds to a cusped wave. par The second case is the socalled modified BenjaminOno equation where the interaction of two solitary waves is investigated. It is found that two solitary waves may interact in such a way that the smaller wave is annihilated. The third case concerns the Benjamin equation which features two competing dispersive operators. In this case, it is found that bifurcation curves of periodic travelingwave solutions may cross and connect high up on the branch in the nonlinear regime. 
Homepage:  https://github.com/olivierverdier/SpecTraVVave 
Keywords:  traveling waves; nonlinear dispersive equations; bifurcation; solitary waves 
Related Software:  RODAS; GitHub; Python; AUTO 
Referenced in:  6 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

A numerical study of nonlinear dispersive wave models with \(\mathsf{SpecTraVVave}\). Zbl 1370.35074 Kalisch, Henrik; Moldabayev, Daulet; Verdier, Olivier 
2017

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Referenced by 9 Authors
2  Kalisch, Henrik 
1  Charalampidis, Efstathios G. 
1  Derzho, Oleg G. 
1  Dinvay, Evgueni 
1  Hildrum, Fredrik 
1  Hur, Vera Mikyoung 
1  Moldabayev, Daulet 
1  Trandal, Krister J. 
1  Verdier, Olivier 
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Referenced in 6 Serials
1  Nonlinearity 
1  Wave Motion 
1  Applied Numerical Mathematics 
1  Electronic Journal of Differential Equations (EJDE) 
1  Chaos 
1  Water Waves 
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Referenced in 6 Fields
5  Fluid mechanics (76XX) 
4  Partial differential equations (35XX) 
1  Integral equations (45XX) 
1  Numerical analysis (65XX) 
1  Relativity and gravitational theory (83XX) 
1  Geophysics (86XX) 