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Journal articles on the topic 'Davey-Stewartson equations'

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Published: 4 June 2021

Last updated: 14 February 2022

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1

Sall?, M. A. "The Davey-Stewartson equations." Journal of Mathematical Sciences 68, no. 2 (1994): 265–70. http://dx.doi.org/10.1007/bf01249340.

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2

Mhlanga, Isaiah Elvis, and Chaudry Masood Khalique. "Exact Solutions of Generalized Boussinesq-Burgers Equations and (2+1)-Dimensional Davey-Stewartson Equations." Journal of Applied Mathematics 2012 (2012): 1–8. http://dx.doi.org/10.1155/2012/389017.

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We study two coupled systems of nonlinear partial differential equations, namely, generalized Boussinesq-Burgers equations and (2+1)-dimensional Davey-Stewartson equations. The Lie symmetry method is utilized to obtain exact solutions of the generalized Boussinesq-Burgers equations. The travelling wave hypothesis approach is used to find exact solutions of the (2+1)-dimensional Davey-Stewartson equations.

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3

Nakao, Takenobu, and Miki Wadati. "Higher-order Davey-Stewartson equations." Chaos, Solitons & Fractals 4, no. 5 (1994): 701–8. http://dx.doi.org/10.1016/0960-0779(94)90078-7.

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4

BRUNELLI, J. C., and ASHOK DAS. "DAVEY-STEWARTSON EQUATION FROM A ZERO CURVATURE AND A SELF-DUALITY CONDITION." Modern Physics Letters A 09, no. 14 (1994): 1267–72. http://dx.doi.org/10.1142/s0217732394001088.

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We derive the two equations of Davey-Stewartson type from a zero curvature condition associated with SL(2, ℝ) in (2+1) dimensions. We show in general how a (2+1)dimensional zero curvature condition can be obtained from the self-duality condition in (3+3) dimensions and show in particular how the Davey-Stewartson equations can be obtained from the self-duality condition associated with SL(2, ℝ) in (3+3) dimensions.

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5

Güngör, F., and Ö. Aykanat. "The generalized Davey-Stewartson equations, its Kac-Moody-Virasoro symmetry algebra and relation to Davey-Stewartson equations." Journal of Mathematical Physics 47, no. 1 (2006): 013510. http://dx.doi.org/10.1063/1.2162147.

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6

Zhao, Yun-Mei, Ying-Hui He, and Yao Long. "The Simplest Equation Method and Its Application for Solving the Nonlinear NLSE, KGZ, GDS, DS, and GZ Equations." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/960798.

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A good idea of finding the exact solutions of the nonlinear evolution equations is introduced. The idea is that the exact solutions of the elliptic-like equations are derived using the simplest equation method and the modified simplest equation method, and then the exact solutions of a class of nonlinear evolution equations which can be converted to the elliptic-like equation using travelling wave reduction are obtained. For example, the perturbed nonlinear Schrödinger’s equation (NLSE), the Klein-Gordon-Zakharov (KGZ) system, the generalized Davey-Stewartson (GDS) equations, the Davey-Stewart

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7

Yurov, A. V. "Bäcklund-Schlesinger transformations for Davey-Stewartson equations." Theoretical and Mathematical Physics 109, no. 3 (1996): 1508–14. http://dx.doi.org/10.1007/bf02073867.

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8

Gilson, C. R., and S. R. Macfarlane. "Dromion solutions of noncommutative Davey–Stewartson equations." Journal of Physics A: Mathematical and Theoretical 42, no. 23 (2009): 235202. http://dx.doi.org/10.1088/1751-8113/42/23/235202.

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9

Jun, Zhang, Guo Bo-ling, and Shen Shou-feng. "Homoclinic orbits of the Davey-Stewartson equations." Applied Mathematics and Mechanics 26, no. 2 (2005): 139–41. http://dx.doi.org/10.1007/bf02438234.

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10

Gao, Yali, Liquan Mei, and Rui Li. "Galerkin methods for the Davey–Stewartson equations." Applied Mathematics and Computation 328 (July 2018): 144–61. http://dx.doi.org/10.1016/j.amc.2018.01.044.

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11

Guil, Francisco, and Manuel Mañas. "Darboux transformations for the Davey—Stewartson equations." Physics Letters A 217, no. 1 (1996): 1–6. http://dx.doi.org/10.1016/0375-9601(96)00304-0.

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12

Zuevsky, A. "Lie-algebraic symmetries of generalized Davey-Stewartson equations." Journal of Physics: Conference Series 532 (September 10, 2014): 012030. http://dx.doi.org/10.1088/1742-6596/532/1/012030.

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13

Malanyuk, T. M. "Finite-zone solutions of Davey-Stewartson 2 equations." Russian Mathematical Surveys 46, no. 5 (1991): 193–94. http://dx.doi.org/10.1070/rm1991v046n05abeh002846.

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14

Kiselev, O. M. "Dromion Perturbation for the Davey-Stewartson-1 Equations." Journal of Nonlinear Mathematical Physics 7, no. 4 (2000): 411–22. http://dx.doi.org/10.2991/jnmp.2000.7.4.1.

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15

Huard, Benoit, and Vladimir Novikov. "On classification of integrable Davey–Stewartson type equations." Journal of Physics A: Mathematical and Theoretical 46, no. 27 (2013): 275202. http://dx.doi.org/10.1088/1751-8113/46/27/275202.

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16

Malanyuk, T. M. "Finite-gap solutions of the Davey-Stewartson equations." Journal of Nonlinear Science 4, no. 1 (1994): 1–21. http://dx.doi.org/10.1007/bf02430624.

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17

Fordy, A., and C. Athorne. "Generalized Davey-Stewartson equations associated with symmetric spaces." Physica D: Nonlinear Phenomena 28, no. 1-2 (1987): 248. http://dx.doi.org/10.1016/0167-2789(87)90206-5.

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18

Hao, Cheng-chun. "Energy Scattering for the Generalized Davey-Stewartson Equations." Acta Mathematicae Applicatae Sinica, English Series 19, no. 2 (2003): 333–40. http://dx.doi.org/10.1007/s10255-003-0108-0.

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19

Jafari, H., K. Sayevand, Yasir Khan, and M. Nazari. "Davey-Stewartson Equation with Fractional Coordinate Derivatives." Scientific World Journal 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/941645.

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We have used the homotopy analysis method (HAM) to obtain solution of Davey-Stewartson equations of fractional order. The fractional derivative is described in the Caputo sense. The results obtained by this method have been compared with the exact solutions. Stability and convergence of the proposed approach is investigated. The effects of fractional derivatives for the systems under consideration are discussed. Furthermore, comparisons indicate that there is a very good agreement between the solutions of homotopy analysis method and the exact solutions in terms of accuracy.

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20

Zedan, H. A., and S. Sh Tantawy. "Solution of Davey-Stewartson equations by homotopy perturbation method." Computational Mathematics and Mathematical Physics 49, no. 8 (2009): 1382–88. http://dx.doi.org/10.1134/s0965542509080089.

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21

Boling, Guo, and Li Yongsheng. "Long time behavior of solutions of Davey-Stewartson equations." Acta Mathematicae Applicatae Sinica 17, no. 1 (2001): 86–97. http://dx.doi.org/10.1007/bf02669688.

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22

Carles, Rémi, and Clément Gallo. "WKB analysis of nonelliptic nonlinear Schrödinger equations." Communications in Contemporary Mathematics 22, no. 06 (2019): 1950045. http://dx.doi.org/10.1142/s0219199719500457.

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We justify the WKB analysis for generalized nonlinear Schrödinger equations (NLS), including the hyperbolic NLS and the Davey–Stewartson II system. Since the leading order system in this analysis is not hyperbolic, we work with analytic regularity, with a radius of analyticity decaying with time, in order to obtain better energy estimates. This provides qualitative information regarding equations for which global well-posedness in Sobolev spaces is widely open.

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23

Rao, J., Y. Cheng, and J. He. "Rational and Semirational Solutions of the Nonlocal Davey-Stewartson Equations." Studies in Applied Mathematics 139, no. 4 (2017): 568–98. http://dx.doi.org/10.1111/sapm.12178.

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24

Leble, S. B., M. A. Salle, and A. V. Yurov. "Darboux transforms for Davey-Stewartson equations and solitons in multidimensions." Inverse Problems 8, no. 2 (1992): 207–18. http://dx.doi.org/10.1088/0266-5611/8/2/004.

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25

Taimanov, Iskander A. "Surfaces in the four-space and the Davey–Stewartson equations." Journal of Geometry and Physics 56, no. 8 (2006): 1235–56. http://dx.doi.org/10.1016/j.geomphys.2005.06.013.

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26

Groves, Mark D., Shu-Ming Sun, and Erik Wahlén. "Periodic solitons for the elliptic–elliptic focussing Davey–Stewartson equations." Comptes Rendus Mathematique 354, no. 5 (2016): 486–92. http://dx.doi.org/10.1016/j.crma.2016.02.005.

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27

Jafari, H., H. Tajadodi, A. Bolandtalat, and S. J. Johnston. "A Decomposition Method for Solving the Fractional Davey-Stewartson Equations." International Journal of Applied and Computational Mathematics 1, no. 4 (2015): 559–68. http://dx.doi.org/10.1007/s40819-015-0031-0.

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28

Zedan, Hassan A., W. Barakati, and Nada Hamad. "The Application of the Homotopy Analysis Method and the Homotopy Perturbation Method to the Davey-Stewartson Equations and Comparison between Them and Exact Solutions." Journal of Applied Mathematics 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/326473.

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We introduce two powerful methods to solve the Davey-Stewartson equations: one is the homotopy perturbation method (HPM) and the other is the homotopy analysis method (HAM). HAM is a strong and easy to use analytic tool for nonlinear problems. Comparison of the HPM results with the HAM results, and compute the absolute errors between the exact solutions of the DS equations with the HPM solutions and HAM solutions are obtained.

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29

Hassan, M. M., and A. H. Khater. "Jacobi Elliptic Function Solutions of Three Coupled Nonlinear Physical Equations." Zeitschrift für Naturforschung A 60, no. 4 (2005): 237–44. http://dx.doi.org/10.1515/zna-2005-0404.

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Abstract The Jacobi elliptic function solutions of coupled nonlinear partial differential equations, including the coupled modified KdV (mKdV) equations, long-short-wave interaction system and the Davey- Stewartson (DS) equations, are obtained by using the mixed dn-sn method. The solutions obtained in this paper include the single and the combined Jacobi elliptic function solutions. In the limiting case, the solitary wave solutions of the systems are also given. - PACS: 02.30.Jr; 03.40.Kf; 03.65.Fd

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30

Fan, Engui, and Y. C. Hona. "Generalized tanh Method Extended to Special Types of Nonlinear Equations." Zeitschrift für Naturforschung A 57, no. 8 (2002): 692–700. http://dx.doi.org/10.1515/zna-2002-0809.

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By some ‘pre-possessing’ techniques we extend the generalized tanh method to special types of nonlinear equations for constructing their multiple travelling wave solutions. The efficiency of the method can be demonstrated for a large variety of special equations such as those considered in this paper, double sine-Gordon equation, (2+1)-dimensional sine-Gordon equation, Dodd-Bullough- Mikhailov equation, coupled Schrödinger-KdV equation and (2+1)-dimensional coupled Davey- Stewartson equation. - Pacs: 03.40.Kf; 02.30.Jr.

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31

Klein, C., and K. Roidot. "Fourth Order Time-Stepping for Kadomtsev–Petviashvili and Davey–Stewartson Equations." SIAM Journal on Scientific Computing 33, no. 6 (2011): 3333–56. http://dx.doi.org/10.1137/100816663.

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32

Li, Yongsheng, and Boling Guo. "EXISTENCE AND DECAY OF WEAK SOLUTIONS TO DEGENERATE DAVEY-STEWARTSON EQUATIONS." Acta Mathematica Scientia 22, no. 3 (2002): 302–10. http://dx.doi.org/10.1016/s0252-9602(17)30299-0.

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33

Li, Yongsheng, Boling Guo, and Murong Jiang. "Existence and blow-up of solutions to degenerate Davey–Stewartson equations." Journal of Mathematical Physics 41, no. 5 (2000): 2943–56. http://dx.doi.org/10.1063/1.533282.

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34

Serikbayev, N. S., G. N. Shaikhova, K. R. Yesmakhanova, and R. Myrzakulov. "Traveling wave solutions for the (3+1)-dimensional Davey-Stewartson equations." Journal of Physics: Conference Series 1391 (November 2019): 012166. http://dx.doi.org/10.1088/1742-6596/1391/1/012166.

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35

Sung, L. Y. "An Inverse Scattering Transform for the Davey-Stewartson-II Equations, I." Journal of Mathematical Analysis and Applications 183, no. 1 (1994): 121–54. http://dx.doi.org/10.1006/jmaa.1994.1136.

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36

Sung, L. Y. "An Inverse Scattering Transform for the Davey-Stewartson II Equations II." Journal of Mathematical Analysis and Applications 183, no. 2 (1994): 289–325. http://dx.doi.org/10.1006/jmaa.1994.1145.

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37

Sung, L. Y. "An Inverse Scattering Transform for the Davey-Stewartson II Equations, III." Journal of Mathematical Analysis and Applications 183, no. 3 (1994): 477–94. http://dx.doi.org/10.1006/jmaa.1994.1155.

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38

Chen, Wei-Zhong. "Similarity Reductions for the Davey–Stewartson Equations Using a Direct Method." Communications in Theoretical Physics 22, no. 2 (1994): 183–86. http://dx.doi.org/10.1088/0253-6102/22/2/183.

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39

Champagne, B., and P. Winternitz. "On the infinite‐dimensional symmetry group of the Davey–Stewartson equations." Journal of Mathematical Physics 29, no. 1 (1988): 1–8. http://dx.doi.org/10.1063/1.528173.

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40

Rosenhaus, V., and M. Gandarias. "On conserved densities and boundary conditions for the Davey–Stewartson equations." Journal of Physics A: Mathematical and Theoretical 43, no. 4 (2010): 045206. http://dx.doi.org/10.1088/1751-8113/43/4/045206.

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41

El-Ganaini, Shoukry Ibrahim Atia. "New Exact Solutions of Some Nonlinear Systems of Partial Differential Equations Using the First Integral Method." Abstract and Applied Analysis 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/693076.

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The first integral method introduced by Feng is adopted for solving some important nonlinear systems of partial differential equations, including classical Drinfel'd-Sokolov-Wilson system (DSWE), (2 + 1)-dimensional Davey-Stewartson system, and generalized Hirota-Satsuma coupled KdV system. This method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are formally derived in a concise manner. This method can also be applied to nonintegrable equations as well as integrable ones.

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42

Roy Chowdhury, K., and A. Roy Chowdhuy. "Nonlinear Equation in (2+1) Dimensions for a Plasma with Negative Ions." Australian Journal of Physics 49, no. 6 (1996): 1159. http://dx.doi.org/10.1071/ph961159.

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A new form of coupled nonlinear evolution equation is derived for a plasma with negative ions in (2+1) dimensions. This system of equations can be considered to be an extension of the usual Davey–Stewartson equation. A modified version of reductive perturbation has been used. It is also shown that this set of equations can sustain both cnoidal type and the usual solitary wave-like solution. Such an equation can have important applications in describing nonlinear wave propagation in a dusty plasma.

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43

Liu, Changfu, Chuanjian Wang, Zhengde Dai, and Jun Liu. "New Rational Homoclinic and Rogue Waves for Davey-Stewartson Equation." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/572863.

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A new method, homoclinic breather limit method (HBLM), for seeking rogue wave solution of nonlinear evolution equation is proposed. A new family of homoclinic breather wave solution, and rational homoclinic solution (homoclinic rogue wave) for DSI and DSII equations are obtained using the extended homoclinic test method and homoclinic breather limit method (HBLM), respectively. Moreover, rogue wave solution is exhibited as period of periodic wave in homoclinic breather wave approaches to infinite. This result shows that rogue wave can be generated by extreme behavior of homoclinic breather wav

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44

Jafari, H., and M. Alipour. "Solution of the Davey–Stewardson equation using homotopuy analysis method." Nonlinear Analysis: Modelling and Control 15, no. 4 (2010): 423–33. http://dx.doi.org/10.15388/na.15.4.14313.

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In this paper, the homotopy analysis method (HAM) proposed by Liao is adopted for solving Davey–Stewartson (DS) equations which arise as higher dimensional generalizations of the nonlinear Schrödinger (NLS) equation. The results obtained by HAM have been compared with the exact solutions and homotopy perturbation method (HPM) to show the accuracy of the method. Comparisons indicate that there is a very good agreement between the HAM solutions and the exact solutions in terms of accuracy.

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45

Klein, C., and K. Roidot. "Numerical study of the semiclassical limit of the Davey–Stewartson II equations." Nonlinearity 27, no. 9 (2014): 2177–214. http://dx.doi.org/10.1088/0951-7715/27/9/2177.

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46

Guo, Yanqiu, Irma Hacinliyan, and Edriss S. Titi. "Non-viscous regularization of the Davey-Stewartson equations: Analysis and modulation theory." Journal of Mathematical Physics 57, no. 8 (2016): 081502. http://dx.doi.org/10.1063/1.4960047.

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47

Guo, Cuihua, and Shangbin Cui. "A note on the Cauchy problem of the generalized Davey–Stewartson equations." Applied Mathematics and Computation 215, no. 6 (2009): 2262–68. http://dx.doi.org/10.1016/j.amc.2009.08.038.

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48

Yang, Bo, and Yong Chen. "Reductions of Darboux transformations for the PT-symmetric nonlocal Davey–Stewartson equations." Applied Mathematics Letters 82 (August 2018): 43–49. http://dx.doi.org/10.1016/j.aml.2017.12.025.

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49

Sung, L. Y. "Long-time decay of the solutions of the Davey?Stewartson II equations." Journal of Nonlinear Science 5, no. 5 (1995): 433–52. http://dx.doi.org/10.1007/bf01212909.

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50

Pelinovsky, Dmitry. "On a structure of the explicit solutions to the Davey-Stewartson equations." Physica D: Nonlinear Phenomena 87, no. 1-4 (1995): 115–22. http://dx.doi.org/10.1016/0167-2789(95)00158-z.

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