×

zbMATH — the first resource for mathematics

Perturbation of topological solitons due to sine-Gordon equation and its type. (English) Zbl 1221.37121
Summary: We study the adiabatic dynamics of topological solitons in presence of perturbation terms. The solitons due to sine-Gordon equation, double sine-Gordon equation, sine-cosine Gordon equation and double sine-cosine Gordon equations are studied, in this paper. The adiabatic variation of soliton velocity is obtained in this paper by soliton perturbation theory.

MSC:
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q51 Soliton equations
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
35Q55 NLS equations (nonlinear Schrödinger equations)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abdullaev, F., Theory of solitons in inhomogenous media, (1994), John Wiley and Sons New York, NY, USA
[2] Ablowitz, M.J.; Segur, H., Solitons and the inverse scattering transform, (1981), SIAM Philadelphia, PA, USA · Zbl 0472.35002
[3] Bin, H.; Qing, M.; Yao, L.; Weiguo, R., New exact solutions of the double sine-Gordon equation using symbolic computations, Appl math comput, 186, 2, 1334-1346, (2007) · Zbl 1117.65133
[4] Chacon, R., Reshaping-induced spatiotemporal chaos in driven, damped sine-Gordon systems, Chaos solitons fract, 31, 5, 1265-1271, (2007)
[5] Christov, I.; Christov, C.I., Physical dynamics of quasi-particles in nonlinear wave equations, Phys lett A, 372, 6, 841-848, (2008) · Zbl 1217.81052
[6] Dauxois, T.; Peyrard, M., Physics of solitons, (2006), Cambridge University Press England, UK · Zbl 1192.35001
[7] Feng, Z., Exact solution to an approximate sine-Gordon equation in the (n+1)-dimensional space, Phys lett A, 302, 2-3, 64-76, (2002) · Zbl 0998.35046
[8] Fokas, A.; Zakharov, V.E., Important developments in soliton theory, (1993), Springer Verlag New York, NY, USA · Zbl 0801.00009
[9] Kivshar, Y.S.; Malomed, B.A., Three particle and inelastic effects in the interaction of conservatively perturbed sine-Gordon equation kinks, Phys lett A, 115, 8, 381-384, (1986)
[10] Kivshar, Y.S.; Malomed, B.A., Dynamics of solitons in nearly integrable systems, Rev modern phys, 61, 4, 763-915, (1989)
[11] Kodama, Y.; Ablowitz, M.J., Perturbations of solitons and solitary waves, Stud appl math, 64, 225-245, (1981) · Zbl 0486.76029
[12] Li, L.; Li, M., Bounded travelling wave solutions for the (n+1)-dimensional sine- and sinh-Gordon equations, Chaos solitons fract, 25, 5, 1037-1047, (2005) · Zbl 1070.35068
[13] Liu, S.; Fu, Z.; Liu, S., Exact solution to sine-Gordon type equations, Phys lett A, 351, 1-2, 59-63, (2006) · Zbl 1234.35227
[14] Manton, N.; Sutcliffe, P., Topological solitons, (2007), Cambridge University Press England, UK
[15] Maksimov, A.G.; Pedersen, N.F.; Christiansen, P.L.; Molkov, J.I.; Nekorkin, V.I., On kink dynamics of the perturbed sine-Gordon equation, Wave motion, 23, 203-213, (1996) · Zbl 0920.35137
[16] Panigrahi, M.; Dash, P.C., Mixing exponential and double sine-Gordon equation, Phys lett A, 321, 330-334, (2004) · Zbl 1118.81421
[17] Popov, C.A., Perturbation theory for the double sine-Gordon equation, Wave motion, 42, 4, 309-316, (2005) · Zbl 1189.35287
[18] Riazi, N.; Gharaati, A.R., Dynamics of sine-Gordon solitons, Int J theor phys, 37, 3, 1081-1120, (1998) · Zbl 0929.35139
[19] Sirendaoreji; Jiong, S., A direct method for solving sine-Gordon type equations, Phys lett A, 298, 2-3, 133-139, (2002) · Zbl 0995.35056
[20] Skiniotis, T.; Bountis, T., Soliton propagation in a system of two inductively coupled long Josephson junctions, Chaos solitons fract, 5, 12, 2571-2584, (1995) · Zbl 1080.82588
[21] Smyth, N.F.; Worthy, A.L., Soliton evolution and radiation loss for the sine-Gordon equation, Phys rev E, 60, 2, 2330-2336, (1999)
[22] Wang, M.; Li, X., Exact solutions to the double sine-Gordon equation, Chaos solitons fract, 27, 2, 477-486, (2006) · Zbl 1088.35543
[23] Wazwaz, A.M., The tanh method: exact solutions of the sine-Gordon and the sinh-Gordon equations, Appl math comput, 167, 2, 1196-1210, (2005) · Zbl 1082.65585
[24] Wazwaz, A.M., Exact solutions to the double sinh-Gordon equation by the tanh method and a variable separated ODE method, Comput math appl, 50, 10-12, 1685-1696, (2005) · Zbl 1089.35534
[25] Wazwaz, A.M., The variable separated ODE and the tanh methods for solving the combined and the double combined sinh – cosh-Gordon equation, Appl math comput, 177, 2, 745-754, (2006) · Zbl 1096.65104
[26] Wazwaz, A.M., Travelling wave solutions for the combined and double combined sine – cosine-Gordon equations by the variable separated ODE method, Appl math comput, 177, 2, 755-760, (2006) · Zbl 1099.65095
[27] Wazwaz, A.M., Travelling wave solutions for the mkdv – sine-Gordon and the mkdv – sinh-Gordon equations by using a variable separated ODE method, Appl math comput, 181, 2, 1713-1719, (2006) · Zbl 1105.65096
[28] Wazwaz, A.M., Exact solution of the generalized sine-Gordon and the generalized sinh-Gordon equations, Chaos solitons fract, 28, 1, 127-135, (2006) · Zbl 1088.35544
[29] Wazwaz, A.M., The tanh method and a variable separated ODE method for solving double sine-Gordon equation, Phys lett A, 350, 5-6, 367-370, (2006) · Zbl 1195.65210
[30] Wazwaz, A.M., The tanh method for travelling wave solutions to the zhiber – shabat equation and other related equations, Commun nonlinear sci numer simulat, 13, 3, 584-592, (2008) · Zbl 1155.35446
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.