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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, 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 equations (Korteweg-de Vries equations)
35Q51 Soliton equations
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[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., ()
[4] Yan, Z.Y., Commun. theor. phys, 36, 1, (2001)
[5] Rosenau, P.; Hyman, J.M., Phys. rev. lett, 70, 5, 564, (1993)
[6] Wazwaz, A.M., Appl. math. comput, 123, 2, 205, (2001)
[7] Wazwaz, A.M., Chaos, soliton & fractals, 12, 8, 1549, (2001) · Zbl 1022.35051
[8] Wazwaz, A.M., A first course in integral equations, (1997), World Scientific Singapore
[9] Adomian, G., Solving frontier problems of physics: the decomposition method, (1994), Kluwer Academic Publishers Boston · Zbl 0802.65122
[10] Adomian, G., J. math. anal. appl, 135, 501, (1998)
[11] Rosenau, P., Phys. rev. lett, 73, 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, 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, 6, 067601, (2002)
[21] Dinda, P.; Remoissenet, M., Phys. rev. E, 60, 5, 6218, (1999)
[22] Byrd, P.F.; Rriedman, M.D., Handbook of elliptic integrals for engineers and scientists, (1971), Springer New York · Zbl 0213.16602
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