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Lumps and rogue waves of generalized Nizhnik–Novikov–Veselov equation

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Abstract

We investigate the generalized \((2+1)\) Nizhnik–Novikov–Veselov equation and construct its linear eigenvalue problem in the coordinate space from the results of singularity structure analysis thereby dispelling the notion of weak Lax pair. We then exploit the Lax pair employing Darboux transformation and generate lumps and rogue waves. The dynamics of lumps and rogue waves is then investigated.

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Acknowledgements

R. S wishes to thank Department of Atomic Energy - National Board of Higher Mathematics (DAE-NBHM) for providing a Junior Research Fellowship. R. R. acknowledges DST (Grant No. SR/S2/HEP-26/2012), Council of Scientific and Industrial Research (CSIR), India (Grant 03(1323)/14/EMR-II dated 03.11.2014) and Department of Atomic Energy - National Board of Higher Mathematics (DAE-NBHM), India (Grant 2/48(21)/2014/NBHM(R.P.) /R & D II/15451) for financial support in the form of Major Research Projects. The research of P. G. E has been supported in part by MINECO (Grants MAT2013-46308 and MAT2016-75955) and Junta de Castilla y León (Grant SA226U13). P. Albares acknowledges a fellowship from the Junta de Castilla y León.

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Authors and Affiliations

  1. Departamento de Física Fundamental, Universidad de Salamanca, 37008, Salamanca, Spain

    P. Albares & P. G. Estevez

  2. Centre for Nonlinear Science (CeNSc), Post-Graduate and Research Department of Physics, Government College for Women (Autonomous), Kumbakonam, 612001, India

    R. Radha & R. Saranya

  3. Post-Graduate and Research Department of Mathematics, Government College for Women (Autonomous), Kumbakonam, 612001, India

    R. Saranya

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  1. P. Albares
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  2. P. G. Estevez
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  3. R. Radha
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  4. R. Saranya
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Correspondence to R. Radha.

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Albares, P., Estevez, P.G., Radha, R. et al. Lumps and rogue waves of generalized Nizhnik–Novikov–Veselov equation. Nonlinear Dyn 90, 2305–2315 (2017). https://doi.org/10.1007/s11071-017-3804-7

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