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)
A note on “On explicit exact solutions for the Liénard equation and its applications”. (English) Zbl 1098.35563
Summary: Feng $\lbrack$Phys. Lett. A 293 (2002) 50$\rbrack$ obtained a kind of explicit exact solutions to the Liénard equation, and applied these results to find some explicit exact solitary wave solutions to the nonlinear Schrödinger equation and the Pochhammer-Chree equation. In this Letter, more explicit exact solitary wave solutions for the generalized Pochhammer-Chree equation are given by seeking qualitatively the homoclinic or heteroclinic orbits for this class of Liénard equation. Our results extended or improved the results in $\lbrack$Phys. Lett. A 293 (2002) 50; Acta Math. Appl. Sinica 21 (2) (1998) 249; Comput. Phys. Commun. 13 (1977) 149; Phys. Lett. A 196 (1995) 301; Stud. Appl. Math. 75 (1986) 95$\rbrack$.

35Q55NLS-like (nonlinear Schrödinger) equations
Full Text: DOI
[1] Feng, Z. S.: Phys. lett. A. 293, 50 (2002)
[2] Zhang, W. G.: Acta math. Appl. sinica. 21, No. 2, 249 (1998)
[3] Bogolubsky, I. L.: Comput. phys. Commun.. 13, 149 (1977)
[4] Kong, D.: Phys. lett. A. 196, 301 (1995)
[5] Clarkson, P. A.; Leveque, R. J.; Saxton, R.: Stud. appl. Math.. 75, 95 (1986)
[6] W. Wang, J.H. Sun, G.R. Chen, Exact solutions and non-smooth behavior of solitary waves in the generalized non-linear Schrödinger equation, Preprint, 2002
[7] Chow, S. N.; Hale, J. K.: Methods of bifurcation theory. (1982) · Zbl 0487.47039
[8] Guckenheimer, J.; Holmes, P.: Nonlinear oscillations, dynamical systems and bifurcations of vector fields. (1983) · Zbl 0515.34001