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

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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. A characterization of the ground states and the orbital instability of the solitary waves are also established.

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Acknowledgements

This work is part of the Ph.D. Thesis of the first author, which was concluded at IMECC-UNICAMP. The first author acknowledges the financial support from Capes/Brazil and CNPq/Brazil. The second author is partially supported by CNPq/Brazil Grants 402849/2016-7 and 303762/2019-5.

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  1. IMECC-Unicamp, Rua Sérgio Buarque de Holanda 651, Campinas, SP, 13083-859, Brazil

    Andressa Gomes & Ademir Pastor

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  1. Andressa Gomes
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  2. Ademir Pastor
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Correspondence to Ademir Pastor.

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Gomes, A., Pastor, A. Solitary wave solutions and global well-posedness for a coupled system of gKdV equations. J. Evol. Equ. 21, 2167–2193 (2021). https://doi.org/10.1007/s00028-021-00676-4

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