# 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)
Integral approach to compacton solutions of Boussinesq-like $B$($m$,$n$) equation with fully nonlinear dispersion. (English) Zbl 1068.35135
Summary: There exists much good work in the area of usual solitons, but there appears little in the field of compacton solutions. Only a few mathematical tools were employed so far. Recently, {\it Z. Yan} [Chaos Solitons Fractals 14, No. 8, 1151--1158 (2002; Zbl 1038.35082)] extended the decomposition method to seek compacton solutions of $B(m,n)$ equation $u_{tt}=(u^n)_{xx}+(u^m)_{xxx}$. We present a different approach, integral approach, to investigate the compacton solutions of the $B(m,n)$ equation. Not only Yan’s results but also many new compacton solutions of the $B(m,n)$ equation are obtained. Our approach is simple and also suitable for studying compacton solutions of some other equations.

##### MSC:
 35Q53 KdV-like (Korteweg-de Vries) equations 35Q51 Soliton-like equations
Full Text:
##### References:
 [1] Yan, Z. Y.: Commun. theor. Phys. 36, 385 (2001) [2] Yan, Z. Y.: Chaos, soliton & fractals. 14, 1151 (2002) [3] Fermi, E.; Pasta, J. R.; Ulam, S. M.: E.segre journal of collected papers of enrico Fermi. Journal of collected papers of enrico Fermi 2 (1965) [4] Yan, Z. Y.: Commun. theor. Phys. 36, 1 (2001) [5] Rosenau, P.; Hyman, J. M.: Phys. rev. Lett. 70, No. 5, 564 (1993) [6] Wazwaz, A. M.: Appl. math. Comput. 123, No. 2, 205 (2001) [7] Wazwaz, A. M.: Chaos, soliton & fractals. 12, No. 8, 1549 (2001) · Zbl 1022.35051 [8] Wazwaz, A. M.: A first course in integral equations. (1997) · Zbl 0924.45001 [9] Adomian, G.: Solving frontier problems of physics: the decomposition method. (1994) · Zbl 0802.65122 [10] Adomian, G.: J. math. Anal. appl. 135, 501 (1998) [11] Rosenau, P.: Phys. rev. Lett. 73, No. 13, 1737 (1994) [12] Rosenau, P.: Phys. lett. A. 211, 265 (1996) [13] Rosenau, P.: Phys. lett. A. 275, 193 (2000) [14] Dey, B.: Phys. rev. E. 57, No. 4, 4733 (1998) [15] Wazwaz, A. M.: Math. comput. Simul. 56, 269 (2001) [16] Wazwaz, A. M.: Appl. math. Comput. 132, 29 (2002) [17] Wazwaz, A. M.: Chaos, soliton & fractals. 13, 321 (2002) [18] Wazwaz, A. M.: Chaos, soliton & fractals. 13, 1053 (2002) [19] Wazwaz, A. M.: Appl. math. Comput. 134, 487 (2003) [20] Comte, J. C.: Phys. rev. E (3). 65, No. 6, 067601 (2002) [21] Dinda, P.; Remoissenet, M.: Phys. rev. E. 60, No. 5, 6218 (1999) [22] Byrd, P. F.; Rriedman, M. D.: Handbook of elliptic integrals for engineers and scientists. (1971)