zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Exact solutions for a third-order KdV equation with variable coefficients and forcing term. (English) Zbl 1188.35168
Summary: The general projective Riccati equation method and the exp-function method are used to construct generalized soliton solutions and periodic solutions to special KdV equation with variable coefficients and forcing term.

MSC:
35Q53KdV-like (Korteweg-de Vries) equations
WorldCat.org
Full Text: DOI EuDML
References:
[1] N. Nirmala, M. J. Vedan, and B. V. Baby, “Auto-Bäcklund transformation, Lax pairs, and Painlevé property of a variable coefficient Korteweg-de Vries equation,” Journal of Mathematical Physics, vol. 27, no. 11, pp. 2640-2646, 1986. · Zbl 0632.35061 · doi:10.1063/1.527282
[2] E. Fan and Y. C. Hon, “Generalized tanh method extended to special types of nonlinear equations,” Zeitschrift fur Naturforschung A, vol. 57, no. 8, pp. 692-700, 2002.
[3] C. A. Gómez, “Exact solutions for a new fifth-order integrable system,” Revista Colombiana de Matemáticas, vol. 40, no. 2, pp. 119-125, 2006. · Zbl 1189.35274 · emis:journals/RCM/revistas.art810.html · eudml:227601
[4] C. A. Gómez and A. H. Salas, “Exact solutions for a reaction diffusion equation by using the generalized tanh method,” Scientia et Technica, vol. 13, no. 35, pp. 409-410, 2007.
[5] C. A. Gómez, A. H. Salas, and B. Acevedo Frias, “New periodic and soliton solutions for the generalized BBM and Burger/s-BBM equations,” Applied Mathematics and Computation. In press. · Zbl 1203.35221 · doi:10.1016/j.amc.2009.05.068
[6] C. A. Gómez and A. H. Salas, “Exact solutions for a new integrable system (KdV6),” Journal of Mathematical Sciences: Advances and Applications, vol. 1, no. 2, pp. 401-413, 2008. · Zbl 1182.35064
[7] A. H. Salas, C. A. Gómez, and G. Escobar, “Exact solutions for the general fifth order KdV equation by the extended tanh method,” Journal of Mathematical Sciences: Advances and Applications, vol. 1, no. 2, pp. 305-310, 2008. · Zbl 1179.65132
[8] C. A. Gómez, “A new travelling wave solution of the Mikhailov-Novikov-Wang system using the extended tanh method,” Boletín de Matemáticas, vol. 14, no. 1, pp. 38-43, 2007. · Zbl 1203.35219
[9] A.-M. Wazwaz, “The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations,” Applied Mathematics and Computation, vol. 184, no. 2, pp. 1002-1014, 2007. · Zbl 1115.65106 · doi:10.1016/j.amc.2006.07.002
[10] C. A. Gómez, “Special forms of the fifth-order KdV equation with new periodic and soliton solutions,” Applied Mathematics and Computation, vol. 189, no. 2, pp. 1066-1077, 2007. · Zbl 1122.65393 · doi:10.1016/j.amc.2006.11.158
[11] C. A. Gómez and A. H. Salas, “The generalized tanh-coth method to special types of the fifth-order KdV equation,” Applied Mathematics and Computation, vol. 203, no. 2, pp. 873-880, 2008. · Zbl 1154.65364 · doi:10.1016/j.amc.2008.05.105
[12] A. H. Salas and C. A. Gómez, “Computing exact solutions for some fifth KdV equations with forcing term,” Applied Mathematics and Computation, vol. 204, no. 1, pp. 257-260, 2008. · Zbl 1160.35526 · doi:10.1016/j.amc.2008.06.033
[13] C. A. Gómez and A. H. Salas, “The variational iteration method combined with improved generalized tanh-coth method applied to Sawada-Kotera equation,” Applied Mathematics and Computation. In press. · Zbl 1203.65196 · doi:10.1016/j.amc.2009.05.046
[14] J.-H. He and X.-H. Wu, “Exp-function method for nonlinear wave equations,” Chaos, Solitons & Fractals, vol. 30, no. 3, pp. 700-708, 2006. · Zbl 1141.35448 · doi:10.1016/j.chaos.2006.03.020
[15] S. Zhang, “Exp-function method exactly solving the KdV equation with forcing term,” Applied Mathematics and Computation, vol. 197, no. 1, pp. 128-134, 2008. · Zbl 1135.65388 · doi:10.1016/j.amc.2007.07.041
[16] J.-H. He and L.-N. Zhang, “Generalized solitary solution and compacton-like solution of the Jaulent-Miodek equations using the Exp-function method,” Physics Letters A, vol. 372, no. 7, pp. 1044-1047, 2008. · Zbl 1217.35152 · doi:10.1016/j.physleta.2007.08.059
[17] S. Zhang, “Application of Exp-function method to a KdV equation with variable coefficients,” Physics Letters A, vol. 365, no. 5-6, pp. 448-453, 2007. · Zbl 1203.35255 · doi:10.1016/j.physleta.2007.02.004
[18] A. H. Salas, “Exact solutions for the general fifth KdV equation by the exp function method,” Applied Mathematics and Computation, vol. 205, no. 1, pp. 291-297, 2008. · Zbl 1160.35525 · doi:10.1016/j.amc.2008.07.013
[19] A. H. Salas, C. A. Gómez, and J. Castillo, “New abundant solutions for the Burger/s equation,” Computers & Mathematics with Applications, vol. 58, pp. 514-520, 2009.
[20] C. A. Gómez and A. H. Salas, “The Cole-Hopf transformation and improved tanh-coth method applied to new integrable system (KdV6),” Applied Mathematics and Computation, vol. 204, no. 2, pp. 957-962, 2008. · Zbl 1157.65457 · doi:10.1016/j.amc.2008.08.006
[21] R. Conte and M. Musette, “Link between solitary waves and projective Riccati equations,” Journal of Physics. A, vol. 25, no. 21, pp. 5609-5623, 1992. · Zbl 0782.35065 · doi:10.1088/0305-4470/25/21/019
[22] A. H. Salas, “Some solutions for a type of generalized Sawada-Kotera equation,” Applied Mathematics and Computation, vol. 196, no. 2, pp. 812-817, 2008. · Zbl 1132.35461 · doi:10.1016/j.amc.2007.07.013
[23] Z. Yan, “The Riccati equation with variable coefficients expansion algorithm to find more exact solutions of nonlinear differential equations,” MMRC, AMSS, Academis Sinica, vol. 22, pp. 275-284, 2003.
[24] E. Yomba, “The general projective Riccati equations method and exact solutions for a class of nonlinear partial differential equations,” Chinese Journal of Physics, vol. 43, no. 6, pp. 991-1003, 2005.
[25] C. A. Gómez and A. H. Salas, “Special forms of Sawada-Kotera equation with periodic and soliton solutions,” International Journal of Applied Mathematical Analysis and Applications, vol. 3, no. 1, pp. 45-51, 2008. · Zbl 1266.35128
[26] Y. Shang, Y. Huang, and W. Yuan, “New exact traveling wave solutions for the Klein-Gordon-Zakharov equations,” Computers & Mathematics with Applications, vol. 56, no. 5, pp. 1441-1450, 2008. · Zbl 1155.35443 · doi:10.1016/j.camwa.2007.10.033
[27] C. A. Gómez and A. H. Salas, “Exact solutions for the generalized shallow water wave equation by the general projective Riccati equations method,” Boletín de Matemáticas, vol. 13, no. 1, pp. 50-56, 2006. · Zbl 1203.35220
[28] C. A. Gómez and A. H. Salas, “New exact solutions for the combined sinh-cosh-Gordon equation,” Lecturas Matematicas, vol. 27, pp. 87-93, 2006.
[29] C. A. Gómez, “New exact solutions of the Mikhailov-Novikov-Wang system,” International Journal of Computer, Mathematical Sciences and Applications, vol. 1, pp. 137-143, 2007.
[30] Y. Chen and B. Li, “General projective Riccati equation method and exact solutions for generalized KdV-type and KdV-Burgers-type equations with nonlinear terms of any order,” Chaos, Solitons & Fractals, vol. 19, no. 4, pp. 977-984, 2004. · Zbl 1057.35051 · doi:10.1016/S0960-0779(03)00250-9
[31] Taogetusang and Sirendaoerji, “The Jacobi elliptic function-like exact solutions to two kinds of KdV equations with variable coefficients and KdV equation with forcible term,” Chinese Physics, vol. 15, no. 12, pp. 2809-2818, 2006. · doi:10.1088/1009-1963/15/12/008
[32] S.-D. Zhu, “Exp-function method for the Hybrid-Lattice system,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 3, pp. 461-464, 2007.
[33] S.-D. Zhu, “Exp-function method for the discrete mKdV lattice,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 3, pp. 465-468, 2007.
[34] C. Dai, X. Cen, and S. S. Wu, “The application of He/s exp-function method to a nonlinear differential-difference equation,” Chaos, Solitons & Fractals, vol. 41, no. 1, pp. 511-515, 2009. · Zbl 1198.65136 · doi:10.1016/j.chaos.2008.02.021
[35] C.-Q. Dai and J.-F. Zhang, “Application of he/s EXP-function method to the stochastic mKdV equation,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 10, no. 5, pp. 675-680, 2009.