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)
Superposition in nonlinear wave and evolution equations. (English) Zbl 1101.81054
Summary: Real and bounded elliptic solutions suitable for applying the Khare-Sukhatme superposition procedure are presented and used to generate superposition solutions of the generalized modified Kadomtsev-Petviashvili equation (gmKPE) and the nonlinear cubic-quintic Schrödinger equation (NLCQSE)

MSC:
81Q05Closed and approximate solutions to quantum-mechanical equations
35Q55NLS-like (nonlinear Schrödinger) equations
81P05General and philosophical topics in quantum theory
WorldCat.org
Full Text: DOI
References:
[1] Abramowitz, M. and Stegun, I. A. (1972). Handbook of Mathematical Functions, 9th ed., New York, Dover Publications, pp. 651--652. · Zbl 0543.33001
[2] Baldwin, D. et al. (2004). Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs. J. Symb. Comp 37, 669--705. · Zbl 1137.35324 · doi:10.1016/j.jsc.2003.09.004
[3] Bronstein, I. N. et al. (2000). Taschenbuch der Mathematik 5th ed., Thun und Frankfurt am Main, Verlag Harri Deutsch, pp. 40--41.
[4] Chandrasekharan, K. (1985). Elliptic Functions, Berlin, Springer, p. 44. · Zbl 0575.33001
[5] Cooper, F. et al. (2002). Periodic solutions of nonlinear equations obtained by linear superposition. J. Phys. A: Math. Gen 35, 10085--10100. · Zbl 1039.35098 · doi:10.1088/0305-4470/35/47/309
[6] Drazin. P. G. (1983). Solitons, Cambridge, Cambridge University Press, p. 15.
[7] Hereman, W. et al. (1986). Exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method. J. Phys. A: Math. Gen 19, 607--628. · Zbl 0621.35080 · doi:10.1088/0305-4470/19/5/016
[8] Jaworski, M. and Lakshmanan, M. (2003). Comment on ”Linear superposition in nonlinear equations.”Phys. Rev. Lett 90, 239401--1. · doi:10.1103/PhysRevLett.90.239401
[9] Khare, A. and Sukhatme, U. (2002). Cyclic identities involving Jacobi elliptic functions. J. Math. Phys 43, 3798--3806. · Zbl 1060.33026 · doi:10.1063/1.1484541
[10] Khare, A. and Sukhatme, U. (2002). Linear superposition in nonlinear equations. Phys. Rev. Lett 88, 244101-1--244101-4. · doi:10.1103/PhysRevLett.88.244101
[11] Khare, A. et al. (2003). Cyclic identities for Jacobi elliptic and related functions. J. Math. Phys 44, 1822--1841. · Zbl 1062.33020 · doi:10.1063/1.1560856
[12] H. W. (1996). Traveling-wave solutions of the cubic-quintic Schrödinger equation. Phys. Rev. E 54, 4312--4320. · doi:10.1103/PhysRevE.54.4312
[13] Schürmann, H. W. and Serov, V. S. (2004). Traveling wave solutions of a generalized modified Kadomtsev-Petviashvili equation. J. Math. Phys 45, 2181--2817. · Zbl 1071.35115 · doi:10.1063/1.1737813
[14] Schürmann, H. W. and Serov, V. S. (2004). Weierstrass’ solutions to certain nonlinear wave and evolution equations. Proc. Progress in Electromagnetics Research Symposium March 28--31 (Pisa), pp. 651--654.
[15] Wadati, M. et al. (1992). A new hamiltonian amplitude equation governing modulated wave instabilities. J. Phys. Soc. Jpn 61, 1187--1193. · Zbl 1112.35354 · doi:10.1143/JPSJ.61.1187
[16] Weierstrass, K. (1915). Mathematische Werke V, New York, Johnson, pp. 4--16, Whittaker, E. T. and Watson, G. N. (1927) A Course of Modern Analysis, Cambridge, Cambridge University Press, p. 454.