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)
Travelling wave solutions for the generalized Burgers-Huxley equation. (English) Zbl 1160.35515
Summary: Travelling wave solutions for the generalized Burgers-Huxley equation are studied. By using the first-integral method, which is based on the ring theory of commutative algebra, we obtain a class of travelling solitary wave solutions for the generalized Burgers-Huxley equation. A minor error in the literature is clarified.

35Q53KdV-like (Korteweg-de Vries) equations
35C05Solutions of PDE in closed form
35A30Geometric theory for PDE, characteristics, transformations
Full Text: DOI
[1] Wang, M. L.: Exact solutions for a compound KdV-Burgers equation. Phys. lett. A 213, 79-287 (1996) · Zbl 0972.35526
[2] Yang, L.; Liu, J. B.; Yang, K. Q.: Exact solutions of nonlinear PDE, nonlinear transformations and reduction of nonlinear PDE to a quadrature. Phys. lett. A 278, 267-270 (2001) · Zbl 0972.35003
[3] Parkes, E. J.; Duffy, B. R.: Travelling solitary wave solutions to a compound KdV-Burgers equation. Phys. lett. A 229, 217-220 (1997) · Zbl 1043.35521
[4] Fan, E. G.: Extended tanh-function method and its applications to nonlinear equations. Phys. lett. A 277, 212-218 (2000) · Zbl 1167.35331
[5] Fu, Z. T.; Liu, S. K.; Liu, S. D.; Zhao, Q.: New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations. Phys. lett. A 290, 72-76 (2001) · Zbl 0977.35094
[6] Fan, E.; Zhang, J.: Applications of the Jacobi elliptic function method to special-type nonlinear equations. Phys. lett. A 305, 83-392 (2002) · Zbl 1005.35063
[7] Yomba, E.: The extended Fan’s sub-equation method and its applications to KdV -- mkdv, BKK and variant Boussinesq equations. Phys. lett. A 336, 463-476 (2005) · Zbl 1136.35451
[8] Liu, S. K.; Fu, Z. T.; Liu, S. D.: Periodic solutions for a class of coupled nonlinear partial differential equations. Phys. lett. A 336, 175-179 (2005) · Zbl 1136.35459
[9] Ei-Wakil, S. A.; Abdou, M. A.; Elhanbaly, A.: New solitons and periodic wave solutions for nonlinear evolution equations. Phys. lett. A 353, 40-47 (2006)
[10] Zhou, Y. B.; Wang, M. L.; Wang, Y. M.: Periodic wave solutions to a coupled KdV equations with variable coefficients. Phys. lett. A 308, 31-36 (2003) · Zbl 1008.35061
[11] Wang, M. L.; Zhou, Y. B.: The periodic wave solutions for the Klein -- Gordon -- schroinger equations. Phys. lett. A 318, 84-92 (2003) · Zbl 1098.81770
[12] Zhang, S.: New exact solutions of the KdV-Burgers -- Kuramoto equation. Phys. lett. A 358, 414-420 (2006) · Zbl 1142.35592
[13] Yan, Z. Y.; Zhang, H. Q.: New explicit and exact travelling wave solutions for a system of variant Boussinesq equations in mathematical physics. Phys. lett. A 252, No. 3, 291-296 (1999) · Zbl 0938.35130
[14] Wazwaz, A. M.: Solutions of compact and noncompact structures for nonlinear Klein -- Gordon-type equation. Appl. math. Comput. 134, 487-500 (2003) · Zbl 1027.35119
[15] Wazwaz, A. M.: A sine -- cosine method for handling nonlinear wave equations. Math. comput. Model. 40, 499-508 (2004) · Zbl 1112.35352
[16] Tian, L.; Yin, J.: New compacton solutions and solitary wave solutions of fully nonlinear generalized Camassa -- Holm equations. Chaos soliton. Fract. 20, No. 1, 289-299 (2004) · Zbl 1046.35101
[17] Wazwaz, A. M.: Solutions and periodic solutions for the fifth-order KdV equation. Appl. math. Lett. 19, 1162-1167 (2006) · Zbl 1179.35296
[18] Wazwaz, A. M.: Analytic study on nonlinear variant of the RLW and the PHI-four equations. Commun. nonlinear sci. Numer. simul. 12, 314-327 (2007) · Zbl 1109.35099
[19] Yan, Z. Y.: New explicit travelling wave solutions for two new integrable coupled nonlinear evolution equations. Phys. lett. A 292, 100-106 (2001) · Zbl 1092.35524
[20] Wazwaz, A. M.: Travelling wave solutions of generalized forms of Burgers, Burgers-KdV and Burgers -- Huxley equations. Appl. math. Comput. 169, 639-656 (2005) · Zbl 1078.35109
[21] Feng, Z.: The first-integral method to the Burgers-KdV equation. J. phys. A 35, 343-350 (2002) · Zbl 1040.35096
[22] Feng, Z.: On explicit exact solutions to the compound Burgers-KdV equation. Phys. lett. A 293, 57-66 (2002) · Zbl 0984.35138
[23] Feng, Z.: Exact solutions in terms of elliptic functions for the Burgers-KdV equation. Wave motion 38, 109-115 (2003) · Zbl 1163.74349
[24] Z. Feng, Travelling wave behavior for a generalized fisher equation, Chaos Soliton. Fract., 2007. doi:10.1016/j.Chaos.2006.11.031.
[25] Satuma, J.: Topics in soliton theory and exactly solvable nonlinear equations. (1987)
[26] Fitzhugh, R.: Mathematical models of excitation and propagation in nerve. Biological engineering, 1-85 (1969)
[27] Hodgkin, A. L.; Huxley, A. F.: A quantitative description of membrane current and its applications to conduction and excitation in nerve. J. physiol. 117, 500-544 (1952)
[28] Lu, B. Q.; Xiu, B. Z.; Pang, Z. L.; Jiang, X. F.: Exact travelling wave solution of one class of nonlinear diffusion equation. Phys. lett. A 175, 113-115 (1993)
[29] Wang, X. Y.; Zhu, Z. S.; Lu, Y. K.: Solitary wave solutions of the generalized Burgers -- Huxley equation. J. phys. A 23, 271-274 (1990) · Zbl 0708.35079
[30] Ismail, H. N. A.; Raslan, K.; Abd-Rabboh, A. A.: Adomian decomposition method for Burgers -- Huxley and Burgers -- Fisher equation. Appl. math. Comput. 159, 291-301 (2004) · Zbl 1062.65110
[31] Hashim, I.; Noorani, M. S. M.; Al-Hadidi, M. R. Said: Solving the generalized Burgers -- Huxley equation using the Adomian decomposition method. Math. comput. Model. 43, 1404-1411 (2006) · Zbl 1133.65083
[32] Bourbaki, N.: Commutative algebra. (1972) · Zbl 0279.13001
[33] Wang, X. Y.: Exact and explicit solitary wave solutions for the generalized Fisher equation. Phys. lett. A 131, 277-279 (1988)
[34] Yang, Z. J.: Travelling wave solutions to nonlinear evolution and wave equations. J. phys. A: math. Gen. 27, 2837-2855 (1994) · Zbl 0837.35034
[35] Ma, W. X.; Fuchssteiner, B.: Explicit and exact solutions to a KPP equation. Int. J. Nonlinear mech. 31, 329-338 (1996) · Zbl 0863.35106