×

On the coherent structures of the Nizhnik-Novikov-Veselov equation. (English) Zbl 1273.35264

Summary: A variable separation approach is used to obtain exact solutions of high-dimensional nonlinear physical models. Taking the Nizhnik-Novikov-Veselov (NNV) equation as a simple example, we show that a high-dimensional nonlinear physical model may have quite rich localized coherent structures. For the NNV equation, the richness of the localized structures caused by the entrance of two variable-separated arbitrary functions. For some special selections of the arbitrary functions, it is shown that the localized structures of the NNV equation may be dromions, lumps, breathers, instantons and ring solitons, etc.

MSC:

35Q70 PDEs in connection with mechanics of particles and systems of particles
35Q74 PDEs in connection with mechanics of deformable solids
35C05 Solutions to PDEs in closed form
35Q53 KdV equations (Korteweg-de Vries equations)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Lou, S.-y., Comm. Theor. Phys., 33, 7 (2000)
[2] Lou, S.-y., J. Math. Phys., 35, 1755 (1994)
[3] Matveev, V. B.; Salle, M. A., Darboux Transformations and Solitons (1991), Springer: Springer Berlin · Zbl 0744.35045
[4] Lou, S.-y.; Chen, L.-l., J. Math. Phys., 40, 6491 (1999)
[5] Cao, C.-w., Sci. China A, 33, 528 (1990)
[6] Ruan, H.-y.; Chen, Y.-x., Acta Phys. Sinica, 8, 241 (1999)
[7] Novikov, S. P.; Veselov, A. P., Physica D, 18, 267 (1986)
[8] Boiti, M.; Leon, J. J.P.; Manna, M.; Pempinelli, F., Inv. Problems, 2, 116 (1986)
[9] Hu, X.-b.; Li, Y.-s., J. Phys. A: Math. Gen., 24, 1979 (1991)
[10] Hu, X.-b., J. Phys. A: Math. Gen., 27, 1331 (1994)
[11] Radha, R.; Lakshmanan, M., J. Phys. A: Math. Gen., 35, 4746 (1994)
[12] Lou, S.-y., Comm. Theor. Phys., 26, 487 (1996)
[13] Lou, S.-y., J. Math. Phys., 41, 6509 (2000)
[14] Lou, S.-y., J. Phys. A: Math. Gen., 32, 4521 (1999)
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.