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arXiv · 2002.09531

Solitary wave solutions and global well-posedness for a coupled system of gKdV equations

Andressa Gomes·Ademir Pastor
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Abstract

In this work we consider the initial-value problem associated with a coupled system of generalized Korteweg-de Vries equations. We present a relationship between the best constant for a Gagliardo-Nirenberg type inequality and a criterion for the existence of global solutions in the energy space. We prove that such a constant is directly related to the existence problem of solitary-wave solutions with minimal mass, the so called ground state solutions. To guarantee the existence of ground states we use a variational method.

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Andressa Gomes, Ademir Pastor. 2020-02-21. Solitary wave solutions and global well-posedness for a coupled system of gKdV equations. https://arxiv.org/abs/2002.09531

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