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Symmetry analysis of an integrable Itô coupled system. (English) Zbl 1207.35263
Summary: We study the invariance analysis, integrability properties and P-property of the Ito coupled nonlinear partial differential equations. We explore several new solutions for the Ito system through the Lie symmetry analysis. Moreover, this work has been devoted to study the integrability aspects of the Ito system through higher order symmetries. We are also investigating the existence of higher order symmetries for the Ito system. Interestingly our investigations reveal a rich variety of particular solutions, which have not been reported in the literature, for this model.
##### MSC:
 35Q53 KdV-like (Korteweg-de Vries) equations 35A30 Geometric theory for PDE, characteristics, transformations 37K05 Hamiltonian structures, symmetries, variational principles, conservation laws 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
##### References:
 [1] Olver, P. J.: Applications of Lie groups to differential equations, (1986) [2] Bluman, G. W.; Kumei, S.: Symmetries and differential equations, (1989) [3] Stephani, H.: Differential equations: their solutions using symmetries, (1990) [4] Ibrahimov, N. H.: CRC handbook of Lie group analysis of differential equations, (1996) · Zbl 0864.35003 [5] Clarkson, P. A.: Chaos solitons fractals, Chaos solitons fractals 5, 2261 (1995) [6] Ablowitz, M. J.; Segur, A. Ramani: J. math. Phys., J. math. Phys. 21, 715 (1983) [7] Lakshmanan, M.; Sahadevan, R.: Phys. rep., Phys. rep. 224, 1 (1993) [8] Ramani, A.; Grammaticos, B.; Bountis, T.: Phys. rep., Phys. rep. 180, l59 (1989) [9] Head, A.: Comput. phys. Comm., Comput. phys. Comm. 77, 241 (1993) [10] Hone, A. N. W.: Painlevé tests, singularity structure, and integrability, Nonlinear sci., 1-34 (2005) [11] Grammaticos, B.; Dorizzi, B.: Math. comput. Simulation, Math. comput. Simulation 37, No. 4–5, 341-352 (1994) [12] Grammaticos, B.; Ramani, A.; Tamizhmani, K. M.; Tamizhmani, T.; Carstea, A. S.: J. phys. A, J. phys. A 40, No. 30 (2007) [13] Jimbo, M.; Krudkal, M. D.; Miwa, T.: Phys. lett., Phys. lett. 92A, 59-60 (1982) [14] Krudkal, M. D.; Clarkson, P. A.: Stud. appl. Math., Stud. appl. Math. 86, No. 87, 165 (1992) [15] Olver, P. J.; Sokolov, V. V.: Comm. maths. Phys., Comm. maths. Phys. 193, 245 (1998)