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The $\frac{G'}{G}$ method and 1-soliton solution of the Davey-Stewartson equation. (English) Zbl 1217.35171
Summary: This paper studies the Davey-Stewartson equation. The $\frac{G'}{G}$ method is applied to carry out the integration of this equation. Subsequently, using the ansatz method this equation is integrated in $(1+2)$ dimensions with power law nonlinearity.

35Q55NLS-like (nonlinear Schrödinger) equations
35C08Soliton solutions of PDE
Full Text: DOI
[1] Bekir, A.; Cevikel, A. C.: New solitons and periodic solutions for nonlinear physical models in mathematical physics, Nonlinear analysis: real world applications 11, No. 4, 3275-3285 (2010) · Zbl 1196.35178 · doi:10.1016/j.nonrwa.2009.10.015
[2] Caixia, S.; Boling, G.: Ill-posedness for the nonlinear Davey--Stewartson equation, Acta Mathematica scientia 28, No. 1, 117-127 (2008) · Zbl 1150.35068 · doi:10.1016/S0252-9602(08)60012-0
[3] Eden, A.; Erbay, H. A.; Muslu, G. M.: Two remarks on a generalized Davey--Stewartson system, Nonlinear analysis: theory, methods and applications 64, No. 5, 979-986 (2006) · Zbl 1091.35088 · doi:10.1016/j.na.2005.05.052
[4] Eden, A.; Erbay, H. A.; Muslu, G. M.: Closing the gap in the purely elliptic generalized Davey--Stewartson system, Nonlinear analysis: theory, methods and applications 69, No. 8, 2575-2582 (2008) · Zbl 1152.35492 · doi:10.1016/j.na.2007.08.034
[5] Eden, A.; Topaloglu, I. A.: Standing waves for a generalized Davey--Stewartson system: revisited, Applied mathematics letters 21, No. 4, 342-347 (2008) · Zbl 1165.35458 · doi:10.1016/j.aml.2007.04.003
[6] Guo, C.; Cui, S.: A note on the Cauchy problem of the generalized Davey--Stewartson equations, Applied mathematics and computation 215, No. 6, 2262-2268 (2009) · Zbl 1181.35261 · doi:10.1016/j.amc.2009.08.038
[7] Jun, Z.; Bo-Ling, G.; Shou-Feng, S.: Homoclinic orbits of the Davey--Stewartson equation, Applied mathematics and mechanics 26, No. 2, 139-141 (2005) · Zbl 1144.76306 · doi:10.1007/BF02438234
[8] Taimanov, I. A.: Surfaces in the four-space and the Davey--Stewartson equations, Journal of geometry and physics 56, No. 8, 1235-1256 (2006) · Zbl 1103.53031 · doi:10.1016/j.geomphys.2005.06.013
[9] Wang, Y.: The Cauchy problem for the elliptic--hyperbolic Davey--Stewartson system in Sobolev space, Journal of mathematical analysis and applications 367, No. 1, 174-192 (2010) · Zbl 1196.35017
[10] Zhao, X.: Self-similar solutions to a generalized Davey--Stewartson system, Mathematical and computer modelling 50, No. 9--10, 1394-1399 (2009) · Zbl 1185.35272 · doi:10.1016/j.mcm.2009.04.023