Geodesic
Global Bifurcation for the Whitham Equation
M. Ehrnström1 ; H. Kalisch2
1 Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
2 Department of Mathematics, University of Bergen Postbox 7800, 5020 Bergen, Norway
Mathematical modelling of natural phenomena, Tome 8 (2013) no. 5, pp. 13-30.

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We prove the existence of a global bifurcation branch of 2π-periodic, smooth, traveling-wave solutions of the Whitham equation. It is shown that any subset of solutions in the global branch contains a sequence which converges uniformly to some solution of Hölder class Cα, α  1/2. Bifurcation formulas are given, as well as some properties along the global bifurcation branch. In addition, a spectral scheme for computing approximations to those waves is put forward, and several numerical results along the global bifurcation branch are presented, including the presence of a turning point and a ‘highest’, cusped wave. Both analytic and numerical results are compared to traveling-wave solutions of the KdV equation.
DOI : 10.1051/mmnp/20138502

M. Ehrnström 1 ; H. Kalisch 2

1 Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
2 Department of Mathematics, University of Bergen Postbox 7800, 5020 Bergen, Norway 
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M. Ehrnström; H. Kalisch. Global Bifurcation for the Whitham Equation. Mathematical modelling of natural phenomena, Tome 8 (2013) no. 5, pp. 13-30. doi : 10.1051/mmnp/20138502. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20138502/

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