zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
1-soliton solution of the coupled KdV equation and Gear-Grimshaw model. (English) Zbl 1197.35215
Summary: This paper carries out the integration of the coupled KdV equation with power law nonlinearity. The solitary wave ansatz is used to carry out the integration. The domain restrictions of the coefficients of nonlinear and dispersion terms fall out. The results are then supplemented by numerical simulations.

35Q53KdV-like (Korteweg-de Vries) equations
35C08Soliton solutions of PDE
35C05Solutions of PDE in closed form
Full Text: DOI
[1] Antonova, M.; Biswas, A.: Adiabatic parameter dynamics of perturbed solitary waves, Communications in nonlinear science and numerical simulation 14, No. 3, 734-748 (2009) · Zbl 1221.35321 · doi:10.1016/j.cnsns.2007.12.004
[2] Bisognin, E.; Bisognin, V.; Sepulveda, M.; Vera, O.: Coupled system of Korteweg -- de Vries equations type in domains with moving boundaries, Journal of computational and applied mathematics 220, No. 1 -- 2, 290-321 (2008) · Zbl 1158.65056 · doi:10.1016/j.cam.2007.08.008
[3] Kudryashov, N. A.; Loguinova, N. B.: Seven common errors in finding exact solutions of nonlinear differential equations, Communications in nonlinear science and numerical simulation 14, No. 9 -- 10, 3507-3529 (2009) · Zbl 1221.35342 · doi:10.1016/j.cnsns.2009.01.023
[4] Kivshar, Y. S.; Malomed, B. A.: Solitons in a system of coupled Korteweg -- de Vries equations, Wave motion 11, No. 3, 261-269 (1989) · Zbl 0692.76012 · doi:10.1016/0165-2125(89)90005-X
[5] Kivshar, Y.; Malomed, B. A.: Dynamics of solitons in nearly integrable systems, Reviews of modern physics 61, No. 4, 763-915 (1989)
[6] Xiao-Yan, T.; Fei, H.; Sen-Yue, L.: Variable coefficient KdV equation and the analytical diagnosis of a dipole blocking life cycle, Chinese physics letters 23, 887-890 (2006)
[7] H. Triki, M.S. Ismail, Solitary wave solutions for a coupled pair of mKdV equations, Applied Mathematics and Computation, in press, doi:10.1016/j.amc.2009.06.047. · Zbl 1203.65153
[8] Wazwaz, A. M.: The extended tanh method for new solitons for many forms of the fifth-order KdV equations, Applied mathematics and computation 184, No. 2, 1002-1014 (2007) · Zbl 1115.65106 · doi:10.1016/j.amc.2006.07.002
[9] Wazzan, L.: A modified tanh -- coth method for solving KdV and the KdV -- burger’s equation, Communications in nonlinear science and numerical simulation 14, No. 2, 443-450 (2009) · Zbl 1221.35376 · doi:10.1016/j.cnsns.2007.06.011
[10] Zhang, H.: New exact solutions for two generalized Hirota -- satsuma coupled KdV systems, Communications in nonlinear science and numerical simulation 12, No. 7, 1120-1127 (2009)