International Scientific Journal

Authors of this Paper

External Links


With the aid of symbolic computation, we derive new types of variable separation solutions for the (2+1)-dimensional Schwarzian Korteweg-de Vries equation based on an improved mapping approach. Rich coherent structures like the soliton-type, rouge wave-type, and cross-like fractal type structures are presented, and moreover, the fusion interactions of localized structures are graphically investigated. Some of these solutions exhibit a rich dynamic, with a wide variety of qualitative behavior and structures that are exponentially localized.
PAPER REVISED: 2017-09-27
PAPER ACCEPTED: 2017-09-29
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE Issue 4, PAGES [1781 - 1786]
  1. Biswas, A., Solitary Waves for Power Law Regularized Long Wave Equation and R(m, n) Equation, Nonlinear Dyn., 59 (2009), 3, pp. 423-426
  2. Lu, X., Peng, M., Painleve-Integrablity and Explicit Solutions of the General Two-Coupled Nonlinear Schrodinger System in the Optical Fiber Communications, Nonlinear Dyn., 73 (2013), 1-2, pp. 405-410
  3. Wazwaz, A. M., Multiple Soliton Solutions for Three Systems of Broer-Kaup-Kupeshmidt Equations Describing Nonlinear and Dispersive Long Gravity Waves, Mod. Phys. Lett. B., 26 (2012), 20, pp. 125-126
  4. Chen, Y. X., Sech-Type and Gaussian-Type Light Bullet Solutions to the Generalized (3+1)Dimensional Cubic-Quintic Schrodinger Equation in PT-Symmetric Potentials, Nonlinear Dyn., 79 (2015), 1, pp. 427-436
  5. Lou, S. Y., Lu, J., Special Solutions from Variable Separation Approach: Davey Stewartson Equation, J. Phys. A: Math. Gen., 29 (1996), 14, pp. 4209-4215
  6. Zhu, H. P., Saptiotemporal Solitons on Cnoidal Wave Backgrounds in Three Media with Different Dis-tributed Transverse Diffraction and Dispersion, Nonlinear Dyn., 76 (2014), 3, pp. 1651-1659
  7. Huang, L., et al., New Variable Separation Solutions, Localized Structures and Fractals in the (3+1)-Dimensional Nonlinear Burgers System, Acta. Physica Sinica, 56 (2007), 2, pp. 611-619
  8. Zhong, W. P., et al., Special Soliton Structures in the(2+1)-Dimensional Nonlinear Schrodinger Equa-tion with Radially Variable Diffraction and Nonlinearity Coefficients, Phys. Rev. E, 83 (2011), 3, 036603
  9. Zheng, C. L., Localized Coherent Structures with Chaotic and Fractal Behaviors in a (2+1)-Dimensional Modified Dispersive Water-Wave System, Commun. Theor. Phys., 40 (2003), 1, pp. 25-32
  10. Dai, C. Q., et al., Spatial Solitons with the Odd and Even Symmetries in (2+1)-Dimensional Spatially in Homogeneous Cubic-Quintic Nonlinear Media with Transverse W-Shaped Modulation, J. Phys. B: At. Mol. Opt. Phys., 44 (2011), 14, 145401
  11. Zhu, H. P., Nonlinear Tunneling for Controllable Rogue Waves in Two Dimensional Graded Index Wave Guides, Nonlinear Dyn., 72 (2013), 4, pp. 873-882
  12. Kong, L. Q., Dai, C. Q., Some Discussions about Variable Separation of Nonlinear Models Using Ricaati Equation Expansion Method, Nonlinear Dyn., (2015), doi10.1007/s11071-015-2089-y
  13. Cheng-Lin, B., Stochastic Soliton-Like Solutions and Theirs Stochastic Excitations under a (2+1)-Dimensional Stochastic Dispersive Long Wave System, Appl. Math. Comput., 219 (2013), 14, pp. 7795-7804
  14. Zheng, C. L., et al., New Variable Separation Excitations of a (2+1)-Dimensional Broer-Kaup-Kupershmidt System Obtained by an Extended Mapping Approach, Z. Naturforsch A., 59 (2004), 12, pp. 912-918
  15. Kudriashov, K., Pickering, P., Rational Solutions for Schwarzian Integrable Hierarchies, J. Phys. A., 31 (1998), 47, pp. 9505-9518
  16. Toda, K., Yu, S. J., A Study of the Construction of Equations in (2+1) Dimensions, Inverse Problems, 17 (2001), 4, pp. 1053-1060
  17. Toda, K., Yu, S. J., The Investigation into the Schwarz-Korteweg-de Vries Equation and the Schwarz Derivative in (2+1) Dimensions, J. Math. Phys., 41 (2000), 7, pp. 4747-4751
  18. Ramirez, J., et al., The Schwarzian Korteweg-de Vries Equation in (2+1) dimensions, J. Phys. A: Math. Gen., 36 (2003), 5, pp. 1467-1484
  19. Ramirez, J., Romero, J. L., New Classes of Solutions for the Schwarzian Korteweg-de Vries Equation in (2+1) Dimensions, J. Phys. A: Math. Theor., 40 (2007), 16, pp. 4351-4365
  20. Luo, M., Li, L., Almost Periodic Solutions of a (2+1)-Dimensional Schwarzian Korteweg-de Vries Equation, Nonlinear Analysis., 69 (2008), 12, pp. 4452-4460
  21. Aslan, I., Analytic Investigation of the (2+1)-Dimensional Schwarzian Korteweg-de Vries Equation for Traveling Wave Solutions, Appl. Math. Comput., 217 (2011), 12, pp. 6013-6017
  22. Zheng, C. L., et al., Peakon, Compacton and Loop Excitations with Periodic behavior in KdV Type Models Related to Schrodinger System, Phys Lett. A., 340 (2005), 5-6, pp. 397-402
  23. Wen, X. Y., Xu, X. G., Multiple Soliton Solutions and Fusion Interaction Phenomena for the (2+1)-Dimensional Modified Dispersive Water-Wave System, Appl. Math. Comput., 219 (2013), 14, pp. 7730-7740

© 2022 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence