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Existence and linearized stability of solitary waves for a quasilinear Benney system

  • João-Paulo Dias (a1), Mário Figueira (a1) and Filipe Oliveira (a2)

We prove the existence of solitary wave solutions to the quasilinear Benney system

where , –1 < p < +∞ and a, γ > 0. We establish, in particular, the existence of travelling waves with speed arbitrarily large if p < 0 and arbitrarily close to 0 if . We also show the existence of standing waves in the case , with compact support if – 1 < p < 0. Finally, we obtain, under certain conditions, the linearized stability of such solutions.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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