A refined invariant subspace method and applications to evolution equations
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Debnath L. Nonlinear Partial Differential Equations for Scientists and Engineers, 2nd Ed. Boston: Birkhäuser, 2004
Fokas A S, Liu Q M. Nonlinear interaction of travelling waves of nonintegrable equations. Phys Rev Lett, 1994, 72: 3293–3296
Galaktionov V A. Invariant subspaces and new explicit solutions to evolution equations with quadratic nonlinearities. Proc Roy Soc Endin Sect A, 1995, 125: 225–246
Galaktionov V A, Svirshchevskii S R. Exact Solutions and Invarinat Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics. London: Chapman and Hall/CRC, 2007
Hirota R, Grammaticos B, Ramani A. Soliton structure of the Drinfel’d-Sokolov-Wilson equation. J Math Phys, 1986, 27: 1499–1505
King J R. Exact polynomial solutions to some nonlinear diffusion equations. Physica D, 1993, 64: 35–65
Li C X, Ma W X, Liu X J, et al. Wronskian solutions of the Boussinesq equation-solitons, negatons, positons and complexitons. Inverse Problems, 2007, 23: 279–296
Ma W X. Integrability. In: Scott A, ed. Encyclopedia of Nonlinear Science. New York: Taylor & Francis, 2005, 250–253
Ma W X. Wronskian solutions to integrable equations. Discrete Contin Dynam Syst, 2009, Supp: 506–515
Ma W X, Abdeljabbar A, Asaad M G. Wronskian and Grammian solutions to a (3+1)-dimensional generalized KP equation. Appl Math Comput, 2011, 217: 10016–10023
Ma W X, Fan E G. Linear superposition principle applying to Hirota bilinear equations. Comput Math Appl, 2011, 61: 950–959
Ma WX, Huang TW, Zhang Y. A multiple exp-function method for nonlinear differential equations and its application. Phys Scr, 2010, 82: 065003
Ma W X, Li C X, He J S. A second Wronskian formulation of the Boussinesq equation. Nonlinear Anal, 2009, 70: 4245–4258
Ma W X, You Y. Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions. Trans Amer Math Soc, 2005, 357: 1753–1778
Ma W X, Zhang Y, Tang Y N, et al. Hirota bilinear equations with linear subspaces of solutions. Appl Math Comput, 2012, 218: 7174–7183
Olver P J. Applications of Lie Groups to Differential Equations, 2nd Ed. New York: Springer-Verlag, 1993
Qu C Z. Group classification and generalized conditional symmetry reduction of the nonlinear diffusion-convection equation with a nonlinear source. Stud Appl Math, 1997, 99: 107–136
Qu C Z, Ji J N, Wang L Z. Conditional Lie-Bäcklund symmetries and sign-invarints to quasi-linear diffusion equations. Stud Appl Math, 2007, 119: 355–391
Qu C Z, Zhu C R. Classification of coupled systems with two-component nonlinear diffusion equations by the invrainat subspace method. J Phys A Math Theor, 2009, 42: 475201
Shen S F, Qu C Z, Jin Y Y, et al. Maximal dimension of invariant subspaces to systems of nonlinear evolution equations. Chin Ann Math B, 2012, 33: 161–178
Svirshchevskii S R. Lie-Bäcklund symmetries of linear ODEs and generalised separation of variables in nonlinear equations. Phys Lett A, 1995, 199: 344–348
Svirshchevskii S R. Ordinary differential operators possessing invaraint subspaces of polynomial type. Commun Nonlinear Sci Numer Simul, 2004, 9: 105–115
Titov S S. A method of finite-diemnsional rings for solving nonlinear equations of mathematical physics. In: Ivanova T P, ed. Aerodynamics. Saratov: Saratov University, 1988, 104–109
Zhdanov R Z. Conditional Lie-Bäcklund symmetry and reductions of evolution equations. J Phys A Math Gen, 1995, 28: 3841–3850