## THERMAL SCIENCE

International Scientific Journal

### SPATIO-TEMPORAL DYNAMICS AND INTERACTION OF LUMP SOLUTIONS FOR THE (4+1)-D FOKAS EQUATION

**ABSTRACT**

The (4+1)-D Fokas equation is a new and important physical model. Its Hirota's bilinear form with a perturbation parameter is obtained by an appropriate trans-formation. A class of lump solutions and three different forms of spatio-temporal structure are obtained. Meanwhile, the theoretical analysis for the change of spatio-temporal structure is discussed by using the extreme value theory of multivariate function. Finally, the interaction between a stripe soliton and lump solution is discussed, and a new wave phenomenon that the lump solution is swallowed and drowned by the stripe soliton is investigated.

**KEYWORDS**

PAPER SUBMITTED: 2017-09-02

PAPER REVISED: 2017-09-27

PAPER ACCEPTED: 2017-12-15

PUBLISHED ONLINE: 2018-09-10

**THERMAL SCIENCE** YEAR

**2018**, VOLUME

**22**, ISSUE

**4**, PAGES [1823 - 1830]

- He, J.-H., Li, Z. B., Converting Fractional Differential Equations into Partial Differential Equations, Thermal Science, 16 (2012), 2, pp. 331-334
- Craik, A. D. D., Adam, J. A., Evolution in Space and Time of Resonant Wave Triads. I. The 'Pump-Wave Approximation', Proceedings of the Royal Society A, 363 (1978), 1713, pp. 243-255
- Tan, W., et al., Dynamical Analysis of Lump Solution for the (2+1)-Dimensional ITO Equation, Ther-mal Science, 21 (2017), 4, pp. 1673-1679
- He, J.-H., Exp-Function Method for Fractional Differential Equations. International Journal of Nonline-ar Sciences & Numerical Simulation, 14 (2013), 6, pp. 363-366
- Hirota, R., Exact Solution of the Korteweg-de Vries Equation for Multiple Collisions of Solitons, Physi-cal Review Letters, 27 (1971), 18, pp. 1192-1194
- Ma, W. X., Zhou. Y., Lump Solutions to Nonlinear Partial Differential Equations via Hirota Bilinear Forms, International Journal of Modern Physics B, 30 (2016), 28, 1640018
- Tan, W., Dai. Z. D., Spatiotemporal Dynamics of Lump Solution to the (1+1)-Dimensional Benjamin-Ono Equation, Nonlinear Dynamics, 89 (2017), 4, pp. 2723-2728
- Ma, W. X., Lump Solutions to the Kadomtsev-Petviashvili Equation, Physics Letters A, 379 (2015), 36, pp. 197-198
- Wang, C. J, Spatiotemporal Deformation of Lump Solution to (2+1)-Dimensional KdV Equation, Non-linear Dynamics, 84 (2015), 2, pp. 697-702
- Tan, W., Dai. Z. D., Dynamics of Kinky Wave for (3+1)-Dimensional Potential Yu-Toda-Sasa-Fuku-yama Equation, Nonlinear Dynamics, 85 (2016), 2, pp. 817-823
- Tan, W., et al. Emergence and Space-Time Structure of Lump Solution to the (2+ 1)-Dimensional Gen-eralized KP Equation, Pramana, 89 (2017), 5, pp. 77-84
- Fokas, A. S., Integrable Nonlinear Evolution Partial Differential Equations in 4+2 and 3+1 Dimensions. Physical Review Letters, 96 (2006), 19, pp. 190-201
- Doshi, J., Reneker, D. H., Electrospinning Process and Application of Electrospun Fibers, Journal of Electrostatics, 35 (1995), 2, pp. 151-160
- Faraz, N., et al., A Simple Mathematical Model for Prediction of Fibre Size in the Bubble Electrospin-ning. Journal of Computational & Theoretical Nanoscience, 10 (2012), 1, pp. 664-665
- Parrish, I. J., Stone, J. M., Nonlinear Evolution of the Magnetothermal Instability in Two Dimensions, Astrophysical Journal, 633 (2005), 1, pp. 334-348
- Zhang S., et al., Bilinearization and New Multisoliton Solutions for the (4+1)-Dimensional Fokas Equa-tion, Pramana-J. Phys. 86 (2016), 6, pp. 1259-1267
- Dai, Z. D., et al., The Three-Wave Method for Nonlinear Evolution Equations, Nonlinear Science Let-ters A, 1 (2010), 1, pp. 77-82
- Wang, C. J., et al., Interaction Between Kink Solitary Wave and Rogue Wave for (2+1)-Dimensional Burgers Equation, Mediterranean Journal of Mathematics, 13 (2016), 3, pp. 1087-1098