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)
Solitary wave solutions of the modified equal width wave equation. (English) Zbl 1221.65219
Summary: We use a linearized numerical scheme based on finite difference method to obtain solitary wave solutions of the one-dimensional modified equal width (MEW) equation. Two test problems including the motion of a single solitary wave and the interaction of two solitary waves are solved to demonstrate the efficiency of the proposed numerical scheme. The obtained results show that the proposed scheme is an accurate and efficient numerical technique in the case of small space and time steps. A stability analysis of the scheme is also investigated.
MSC:
65M06Finite difference methods (IVP of PDE)
35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations
References:
[1]Morrison, P. J.; Meiss, J. D.; Carey, J. R.: Scattering of RLW solitary waves, Physica D 11, 324-336 (1984) · Zbl 0599.76028 · doi:10.1016/0167-2789(84)90014-9
[2]Pregrine, D. H.: Calculations of the development of an undular bore, J fluid mech 25, 321-330 (1966)
[3]Abdulloev, Kh O.; Bogolubsky, I. L.; Markhankv, V. G.: One more example of inelastic soliton interaction, Phys lett 56A, 427-428 (1976)
[4]Gardner, L. R. T.; Gardner, G. A.: Solitary waves of the equal width wave equation, J comput phys 101, 218-223 (1992) · Zbl 0759.65086 · doi:10.1016/0021-9991(92)90054-3
[5]Archilla, B. G.: A spectral method for the equal width equation, J comput phys 125, 395-402 (1996) · Zbl 0848.65069 · doi:10.1006/jcph.1996.0101
[6]Khalifa, A. K.; Raslan, K. R.: Finite difference methods for the equal width wave equation, J Egyptian math soc 7, No. 2, 239-249 (1999) · Zbl 0937.65094
[7]Zaki, S. I.: A least-squares finite element scheme for the EW equation, Comput meth appl mech engrg 189, 587-594 (2000) · Zbl 0963.76057 · doi:10.1016/S0045-7825(99)00312-6
[8]&idot; Dag; Saka, B.: A cubic B-spline collocation method for the EW equation, Math comput appl 9, No. 3, 381-392 (2004)
[9]Raslan, K. R.: A computational method for the equal width equation, Int J comp math 81, 63-72 (2004) · Zbl 1047.65086 · doi:10.1080/00207160310001614963
[10]Esen, A.: A numerical solution of the equal width wave equation by a lumped Galerkin method, Appl math comput 168, 270-282 (2005) · Zbl 1082.65574 · doi:10.1016/j.amc.2004.08.013
[11]Zaki, S. I.: Solitary wave interactions for the modified equal width equation, Comput phys commun 126, 219-231 (2000) · Zbl 0951.65098 · doi:10.1016/S0010-4655(99)00471-3
[12]Hamdi, S.; Enright, W. H.; Schiesser, W. E.; Gottlieb, J. J.: Exact solutions of the generalized equal width wave equation, Iccsa 2, 725-734 (2003)
[13]Evans, D. J.; Raslan, K. R.: Solitary waves for the generalized equal width (GEW) equation, Int J comp math 82, No. 4, 445-455 (2005) · Zbl 1064.65114 · doi:10.1080/0020716042000272539
[14]Wazwaz, A. M.: The tanh and sine – cosine methods for a reliable treatment of the modified equal width equation and its variants, Commun nonlinear sci numer simul 11, 148-160 (2006) · Zbl 1078.35108 · doi:10.1016/j.cnsns.2004.07.001
[15]Smith, G. D.: Numerical solution of partial differential equations: finite difference methods, (1987)