THERMAL SCIENCE

International Scientific Journal

Hong-Ying Luo

,

Wei TanORCID

,

Zheng-De DaiORCID

,

Jun LiuORCID

KINK DEGENERACY AND ROGUE WAVE FOR POTENTIAL KADOMTSEV-PETVIASHVILI EQUATION

ABSTRACT
A new method called homoclinic breather limit method is proposed to solve the
Potential Kadomtsev-Petviashvili equation, breather kink-wave and periodic
soliton are obtained, and kink degeneracy and new rogue wave are first found in this paper.
KEYWORDS
potential Kadomtsev-Petviashvili equation, rogue wave solution, extended homoclinic test method, kink degeneracy, exp-function method
PAPER SUBMITTED: 2015-01-16
PAPER REVISED: 2015-03-01
PAPER ACCEPTED: 2015-05-12
PUBLISHED ONLINE: 2015-10-25
DOI REFERENCE: https://doi.org/10.2298/TSCI1504429L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2015, VOLUME 19, ISSUE No. 4, PAGES [1429 - 1435]
REFERENCES
[1] Debtnath, L., Non-Linear Partial Differential Equations for Scientist and Engineers, Birkhauser, Boston, USA, 1997, 10.1119/1.14292
[2] Hong T., et al., Bogoliubov Quasiparticles Carried by Dark Solitonic Excitations in Nonuniform Bose- Einstein Condensates, Chinese Phys. Lett., 15 (1998), 3, pp. 550-552, 10.1088/0256-307x/15/8/002
[3] Dai, Z. D., et al., Periodic Bifurcation and Soliton Deflexion for Kadomtsev-Petviashvili Equation, Chin. Phys. Lett., 24 (2007), 6, pp. 1429-1432, 10.1088/0256-307x/24/6/001
[4] Tajiri, M., et al., Periodic Soliton Solutions as Imbricate Series of Rational Solitons: Solutions to the Kadomtsev-Petviashvili Equation with Positive Dispersion, Non-linear Math. Phys., 15 (1997), 4, pp. 350-357, 10.2991/jnmp.1997.4.3-4.9
[5] Dai, Z. D., et al., Homoclinic Bifurcation for Boussinesq Equation with Even Constraint, Chin. Phy. Lett., 23 (2006), 5, pp. 1065-1067, 10.1088/0256-307x/23/5/001
[6] Dai, Z. D., et al., Homoclinic Breather-Wave Solutions for Sine-Gordon Equation, Comm. Non-Linear S-ci. Num. Simul., 14 (2009), 3, pp. 3292-3295, 10.1016/j.cnsns.2009.01.013
[7] Li, D. S. et al., New Soliton-like Solutions to the Potential Kadomstev-Petviashvili (PKP) Equation, Appl. Math. Comput., 46 (2003), 2, pp. 381-384, 10.1016/s0096-3003(02)00588-x
[8] Dai, Z. D., et al., An New Mechanical Feature of Two-Solitary Wave to KdV Equation, Chin. Phys. Lett., 29 (2012), 4, pp. 40201-40207, 10.1088/0256-307x/29/4/040201
[9] Inan, E., Some Exact Solutions to the Potential Kadomtsev-Petviashvili Equation and to a System of Shallow Water Equation, Phys. Lett. A, 35 (2006), 5, pp. 314-322
[10] Zeng, X., Some Exact Periodic Soliton Solutions and Resonance for the Potential Kadomtsev- Petviashvili Equation, Chaos Soliton Fract, 42 (2009), 2, pp. 657-661, 10.1088/1742-6596/96/1/012149
[11] Chen, H., New Multiple Soliton Solutions to the General Burgers-Fisher Equation and the Kuramoto- Sivashinsky Equation, Chaos Solitons Fract, 28 (2004), 1, pp. 71-76, 10.1016/s0960-0779(03)00081-x
[12] Xong, Q., Application of Exp-Function Method to Potential Kadomtsev-Petviashvili Equation, Chaos, Solitons and Fractal, 42 (2009), 6, pp. 2653-2659, 10.1016/j.chaos.2009.03.172
[13] Dai, Z. D., et al., Exact Periodic Kink-Wave and Degenerative Soliton Solutions for Potential Kadomtsev-Petviashvili Equation, Commun Non-linear Sci. Numer Simulat. 15 (2010), 5, pp. 2331-2336, 10.1016/j.cnsns.2009.09.037
[14] Huang, J., et al., Homoclinic Orbits and Periodic Solitons for Boussinesq Equation with Evenconstraint, Chaos Solitons Fract, 38 (2005), 6, pp. 1189-1194, 10.1016/j.chaos.2005.02.025
[15] Darvishi, M. T., Najafi, M., A Modification of Extended Homoclinic Test Approach to Solve the (3+1)- Dimensional Potential-YTSF Equation, Chinese Phys. Lett. 28 (2011) 4, 040202, 10.1088/0256-307x/28/4/040202
[16] He, J.-H. Asymptotic Methods for Solitary Solutions and Compactons, Abstract and Applied Analysis (2012), ID 916793, 10.1155/2012/916793
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KINK DEGENERACY AND ROGUE WAVE FOR POTENTIAL KADOMTSEV-PETVIASHVILI EQUATION

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