THERMAL SCIENCE

International Scientific Journal

Hongcai Ma

,

Xiangmin Meng

,

Hanfang Wu

,

Aiping Deng

A CLASS OF LUMP SOLUTIONS FOR ITO EQUATION

ABSTRACT
In this paper, we investigate the exact solutions for the (1+1)-D Ito equation. Some lump solutions are obtained by using Hirota's bilinear method, and the conditions to guarantee analytical and rational localization of the lump solutions are presented. Suitable choices of the involved parameters guaranteeing analyticity of the solution are given. The 3-D plots with particular choices of the involved parameters are illustrated.
KEYWORDS
Ito equation, Lump solution, solitons, Hirota’s bilinear method
PAPER SUBMITTED: 2018-02-28
PAPER REVISED: 2018-04-22
PAPER ACCEPTED: 2018-06-19
PUBLISHED ONLINE: 2019-09-14
DOI REFERENCE: https://doi.org/10.2298/TSCI1904205M
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Issue 4, PAGES [2205 - 2210]
REFERENCES
  1. Ablowitz, M. A., Clarkson, P. A., Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press, New York, USA, 1991
  2. Shi, C. G., et al., Exact Rational Solutions to a Boussinesq-Like Equation in (1+1)-Dimensions, Applied Mathematics Letters, 48 (2015), Oct., pp. 170-176
  3. Ma, W. X., You, Y., Rational Solutions of the Toda lattice Equation in Casoratian form, Chaos, Solitons & Fractals, 22 (2004), 2, pp. 395-406
  4. Zhang, Y., Ma, W. X., Rational Solutions to a KdV-Like Equation, Applied Mathematics and Computa-tion, 256 (2015), Apr., pp. 252-256
  5. Wang, C., et al., The Breather-Like and Rational Solutions for the Integrable Kadomtsev-Petviashvili-Based System, Advances in Mathematical Physics, 2015 (2015), ID 861069
  6. Xu, Z. H., et al., New Periodic Solitary-Wave Solutions for the Benjiamin Ono Equation, Applied Math-ematics and Computation, 215 (2010), 12, pp. 4439-4442
  7. Fu, Z. T., et al., The JEFE Method and Periodic Solutions of Two Kinds of Nonlinear Wave Equations, Communications in Nonlinear Science and Numerical Simulation, 8 (2003), 2, pp. 67-75
  8. Wang, Z., et al., A Method for Constructing Exact Solutions and Application to Benjamin Ono Equa-tion, Chinese Physics, 14 (2005), 11, pp. 2158-2163
  9. Ma, H. C. et al., Lump Solutions to the (2+1)-Dimensional Shallow Water Wave Equation, Thermal Sci-ence, 21 (2017), 7, pp. 1765-1769
  10. Ma, H. C. et al., Rational Solution to a Shallow Water Wave-Like Equation, Thermal Science, 20 (2016), 3, pp. 875-880
  11. Ma, H. C. et al., Rational Solutions to an Caudrey-Dodd-Gibbon-Sawada-Kotera-like Equation, Thermal Science, 20 (2016), 3, pp. 871-874
  12. Ma, H. C., Deng, A. P., Lump Solution of (2+1)-Dimensional Boussinesq Equation, Communications in Theoretical Physics, 65 (2016), 5, pp. 546-552
  13. Zaharov, V. E., Exact Solutions in the Problem of Parametric Interaction of Three-Dimensional Wave Packets, Doklady Akademii Nauk SSSR, 228 (1976), 6, pp. 1314-1316
  14. Craik, A. D. D., Evolution in Space and Time of Resonant Wave Triads. II. A Class of Exact Solutions, Proceedings of the Royal Society A, 363 (1978), 1713, pp. 257-269
  15. Tan, W., Dai, Z., Dynamics of Kinky Wave for (3+1)-Dimensional Potential Yu-Toda-Sasa-Fukuyama Equation, Nonlinear Dynamics, 85 (2016), 2, pp. 817-823
  16. Kaup, D. J., The Lump Solutions and the Backlund Transformation for the Three-Dimensional Three- Wave Resonant Interaction, Journal of Mathematical Physics, 22 (1981), 6, pp. 1176-1181
  17. Satsuma, J., Two-Dimensional Lumps in Nonlinear Dispersive Systems, Journal of Mathematical Phys-ics, 20 (1979), 7, pp. 1496-1503
  18. Ito, M., An Extension of Nonlinear Evolution Equations of the K-dV (mK-dV) Type to Higher Orders, Journal of the Physical Society of Japan, 49 (1980), 2, pp. 771-778
  19. Liu, H. Z., et al., The Recursion Operator Method for Generalized Symmetries and Backlund Transfor-mations of the Burgers Equations, Journal of Applied Mathematics and Computing, 42 (2013), 1-2, pp. 159-170
  20. Song, L., et al., Rogue Wave for the Benjamin Ono Equation, Advances in Pure Mathematics, 5 (2015), 2, pp. 82-87
  21. Darvishi, M. T., Najafi, M., A Modification of Extended Homoclinic Test Approach to Solve the (3+1)-Dimensional Potential-YTSF Equation, Chinese Physics Letters, 28 (2011), 4, ID 040202
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A class of lump solutions for ito equation

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