[1]
F. Calogero and A. Degasperis, "Spectral Transform and Solitons: Tools to Solve and Investigate Nonlinear Evolution Equations", North-Holland Publishing Co., New York, 1982.
DOI: 10.1007/978-1-4899-2058-4_3
Google Scholar
[2]
I. Christov, "On the Wavelet-Galerkin Solution to the Korteweg-de Vries Equation", Wavelets and Matrix Analysis: REU/VIGRE Student Mini-Conference, July 20, 2004.
Google Scholar
[3]
J. Villegas G., J. Castano B., J. Duarte V. and E. Fierro Y., "Wavelet-Petrov-Galerkin Method for the Numerical Solution of the KdV Equation", Applied Mathematical Sciences, Vol. 6, no. 69, 3411 - 3423, 2012.
DOI: 10.12988/ams.2016.511706
Google Scholar
[4]
Alpert, B. and Beylkin, G. and Gines, D. and Vozovoi, L., Adaptive solution of partial differential equations in multiwavelet bases, J. Comput. Phys., 182(1), p.149–190, 2002.
DOI: 10.1006/jcph.2002.7160
Google Scholar
[5]
Bogdanov, L. V. and Zakharov, V. E. The Boussinesq equation revisited, Physica D, 165, 137â€"162, 2002.
Google Scholar
[6]
Hirota, R. and Satsuma, J., Nonlinear evolution equations generated from the B¨acklund transformation for the Boussinesq equation, Progr. Theor. Phys., Vol. 57, pp. 797â€"807, 1977.
DOI: 10.1143/ptp.57.797
Google Scholar
[7]
Ablowitz, M. J. and Segur, H., Solitons and the Inverse Scattering Transform, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 1981.
Google Scholar
[8]
Quispel, J. R.W., Nijhoff, F.W., and Capel, H.W., Linearization of the Boussinesq equation and the modified Boussinesq equation, Phys. Lett. A, Vol. 91, pp. 143â€"145, 1982.
DOI: 10.1016/0375-9601(82)90817-9
Google Scholar
[9]
Nishitani, T. and Tajiri, M., On similarity solutions of the Boussinesq equation, Phys. Lett. A, Vol. 89, pp. 379â€"380, 1982.
Google Scholar
[10]
Weiss, J., The Painlev´e property and B¨acklund transformations for the sequence of Boussinesq equations, J. Math. Phys., Vol. 26, pp. 258â€"269, 1985.
Google Scholar
[11]
Clarkson, P. A. and Kruskal, M. D., New similarity reductions of the Boussinesq equation, J. Math. Phys., Vol. 30, No. 10, pp. 2201â€"2213, 1989.
DOI: 10.1063/1.528613
Google Scholar
[12]
Levi, D. and Winternitz, P., Nonclassical symmetry reduction: example of the Boussinesq equation, J. Phys. A, Vol. 22, pp. 2915â€"2924, 1989.
Google Scholar
[13]
Clarkson, P. A., Nonclassical symmetry reductions for the Boussinesq equation, Chaos, Solitons and Fractals, Vol. 5, pp. 2261â€"2301, 1995.
DOI: 10.1016/0960-0779(94)e0099-b
Google Scholar
[14]
Kaptsov, O. V., Construction of exact solutions to the Boussinesq equation [in Russian], Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 39, No. 3, pp. 74â€"78, 1998.
Google Scholar
[15]
Polyanin, A. D. and Zaitsev, V. F., Handbook of Nonlinear Partial Differential Equations , Chapman and Hall/CRC, Boca Raton, 2004.
Google Scholar
[16]
S. Mallat, "A wavelet tour of signal processing", Academic Press, 2008.
Google Scholar
[17]
A. Latto, H. L. Resnikoff, E. Tenenbaum, The Evaluation of Connection Coefficients of Compactly SupportedWavelets, Proceedings of the French-USA Workshop on Wavelets and Turbulence at Princeton Unversity, June 1991, Springer-Verlag: 1992.
Google Scholar
[18]
A. Secer, M. Kurulay, M. Bayram and M. Ali Akinlar, An Efficient Computer Application of Sinc-Galerkin Approximation for Nonlinear Boundary Value Problems, Boundary Value Problems 2012, 2012:117.
DOI: 10.1186/1687-2770-2012-117
Google Scholar
[19]
A. Secer and M. Kurulay, Sinc-Galerkin Method and its Applications on Singular Dirichlet-Type Boundary Value Problems, Boundary Value Problems 2012, 2012:126.
DOI: 10.1186/1687-2770-2012-126
Google Scholar