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Exact solitary-wave solutions with compact support for the modified KdV equation. (English) Zbl 1067.35099

Summary: The modified KdV equation, \(u_t + u^{2}u_{x} + u_{xxx} = 0\), which exhibits compactons (solitons with compact support), is investigated. New solitary solutions with compact support are developed by using the decomposition method and the symbolic computation system Maple.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35C05 Solutions to PDEs in closed form
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems

Software:

Maple
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Full Text: DOI

References:

[1] Wadati, M., Introduction to solitons, Pramana: J. phys., 57, 5-6, 841-847, (2001)
[2] Wadati, M., The exact solution of the modified kortweg-de Vries equation, J. phys. soc. jpn., 32, 1681-1687, (1972)
[3] Wadati, M., The modified kortweg-de Vries equation, J. phys. soc. jpn., 34, 1289-1296, (1973) · Zbl 1334.35299
[4] Rosenau, P.; Hyman, J.M., Compactons: solitons with finite wavelengths, Phys. rev. lett., 70, 5, 564-567, (1993) · Zbl 0952.35502
[5] Wazwaz, A.M., New solitary-wave special solutions with compact support for the nonlinear dispersive K(m,n) equations, Chaos, solitons & fractals, 13, 321-330, (2002) · Zbl 1028.35131
[6] Rosenau, P., Nonlinear dispersion and compact structures, Phys. rev. lett., 73, 13, 1737-1741, (1994) · Zbl 0953.35501
[7] Rosenau, P., On nonanalytic solitary waves formed by a nonlinear dispersion, Phys. lett. A, 230, 5/6, 305-318, (1997) · Zbl 1052.35511
[8] Rosenau, P., On a class of nonlinear dispersive-dissipative interactions, Phys. D, 230, 5/6, 535-546, (1998) · Zbl 0938.35172
[9] Adomian, G., Solving frontier problems of physics: the decomposition method, (1994), Kluwer Academic Publishers Boston · Zbl 0802.65122
[10] Adomian, G., A review of the decomposition method in applied mathematics, J. math. anal. appl., 135, 501-544, (1988) · Zbl 0671.34053
[11] Adomian, G., Nonlinear stochastic operator equations, (1986), Academic Press San Diego · Zbl 0614.35013
[12] Wazwaz, A.M., Exact special solutions with solitary patterns for the nonlinear dispersive K(m,n) equations, Chaos, solitons & fractals, 13, 161-170, (2002) · Zbl 1027.35115
[13] Wazwaz, A.M., Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method, Chaos, solitons & fractals, 12, 1549-1556, (2001) · Zbl 1022.35051
[14] Yan, Z.Y., New families of solitons with compact support for Boussinesq-like B(m,n) equations with fully nonlinear dispersion, Chaos, solitons & fractals, 14, 1151-1158, (2002) · Zbl 1038.35082
[15] Zhu, Y.G., Exact special solutions with solitary patterns for Boussinesq-like B(m,n) equations with fully nonlinear dispersion, Chaos, solitons & fractals, 22, 213-220, (2004) · Zbl 1062.35125
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