Transverse linear instability of solitary waves for coupled long-wave-short-wave interaction equations. (English) Zbl 1251.35109
Summary: In this paper, we investigate the transverse linear instability of one-dimensional solitary wave solutions of the coupled system of two-dimensional long-wave-short-wave interaction equations. We show that the one-dimensional solitary waves are linearly unstable to perturbations in the transverse direction if the coefficient of the term associated with transverse effects is negative. This transverse instability condition coincides with the non-existence condition identified in the literature for two-dimensional localized solitary wave solutions of the coupled system.
References:
| [1] | Sulem, C.; Sulem, P., The Nonlinear Equation Self-Focusing and Wave Collapse (1999), Springer-Verlag: Springer-Verlag Toronto · Zbl 0928.35157 |
| [2] | Colin, T. D.; Lannes, D., Duke Math. J., 107, 351-419 (2001) · Zbl 1034.35133 |
| [3] | Babaoglu, C., Chaos Solitons Fractals, 38, 48-54 (2008) · Zbl 1142.35599 |
| [4] | Borluk, H.; Erbay, H. A.; Erbay, S., Appl. Math. Lett., 23, 356-360 (2010) · Zbl 1188.35040 |
| [5] | Djordjevic, V. D.; Redekopp, L. G., J. Fluid Mech., 79, 703-714 (1977) · Zbl 0351.76016 |
| [6] | Ma, Y. C.; Redekopp, L. G., Phys. Fluids, 22, 1872-1876 (1979) · Zbl 0408.76009 |
| [7] | Craik, A. D.D., Wave Interactions and Fluid Flows (1985), Cambridge University Press: Cambridge University Press London · Zbl 0172.56201 |
| [8] | Erbay, S., Chaos Solitons Fractals, 11, 1789-1798 (2000) · Zbl 1023.74023 |
| [9] | Laurencot, P. H., Nonlinear Anal., 24, 509-527 (1995) · Zbl 0841.35109 |
| [10] | Zakharov, V. E.; Rubenchik, A. M., Sov. Phys. JETP, 38, 494-500 (1974) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
