References
- M.J. Ablowitz and P.A. Clarkson. Solitons, Nonlinear Evolution Equations and Inverse Scattering. 2nd edition, Cambridge University Press, 1992.
- M.J. Ablowitz and H. Segur. Solitons and the Inverse Scattering Transform. Society for Industrial and Applied Mathematics, 1981.
- J.L. Bona, S. Vento and F.B. Weissler. Singularity formation and blowup of complex-valued solutions of the modified KdV equation. Discrete Contin. Dyn. Syst., 33:4811–4840, 2013. http://dx.doi.org/10.3934/dcds.2013.33.4811.
- L. Escauriaza, C.E. Kenig, G. Ponce and L. Vega. On uniqueness properties of solutions of the k-generalized KdV equations. J. Funct. Anal., 244(2):504–535, 2007. http://dx.doi.org/10.1016/j.jfa.2006.11.004.
- X. Fan and L. Tian. The existence of solitary waves of singularly perturbed mKdV–KS equation. Chaos Soliton Fractals, 26(4):1111–1118, 2005. http://dx.doi.org/10.1016/j.chaos.2005.02.014.
- N. Fenichel. Geometric singular perturbation theory for ordinary differential equations. J. Differ. Equations, 31(1):53–98, 1979. http://dx.doi.org/10.1016/0022-0396(79)90152-9.
- Y. Fu and Z. Liu. Existence of travelling wavefronts of KdV–Burgers equation. Appl. Math. Lett., 24:897–900, 2011. http://dx.doi.org/10.1016/j.aml.2010.12.047.
- C.S. Gardner, J.M. Greene, M.D. Kruskal and R.M. Miura. Method for solving the Korteweg–de Vries equation. Phys. Rev. Lett., 19(1):1095–1097, 1967. http://dx.doi.org/10.1103/PhysRevLett.19.1095.
- C. Gu, H. Hu and Z. Zhou. Darboux Transformations in Integrable Systems: Theory and Their Applications to Geometry. Springer-Verlag, New York, 2005.
- M.A. Helal and M.S. Mehanna. A comparative study between two different methods for solving the general Korteweg–de Vries equation (GKdV). Chaos Soliton Fractals, 33(3):725–739, 2007. http://dx.doi.org/10.1016/j.chaos.2006.11.011.
- E. Infeld and G. Rowlands. Nonlinear Waves, Solitons and Chaos. Cambridge University Press, 2000.
- C.K.R.T. Jones. Geometric singular perturbation theory. Dyn. Syst., pp. 44–118, 1995.
- E.L. Korotyaev. Estimates for solutions of KDV on the phase space of periodic distributions in terms of action variables. Discrete Contin. Dyn. Syst., 30(7):219–225, 2011. http://dx.doi.org/10.3934/dcds.2011.30.219.
- S. Kutluaya and Y. Ucara. A quadratic B-spline Galerkin approach for solving a coupled KdV equation. Math. Model. Anal., 18(1):103–121, 2013. http://dx.doi.org/10.3846/13926292.2013.760011.
- Z. Liu and C. Yang. The application of bifurcation method to a higher-order kdv equation. J. Math. Anal. Appl., 275(1):1–12, 2002. http://dx.doi.org/10.1016/S0022-247X(02)00210-X.
- Y. Martel and F. Merle. Refined asymptotics around solitons for gKdV equations. Discrete Contin. Dyn. Syst., 20(2):177–218, 2008. http://dx.doi.org/10.3934/dcds.2008.20.177.
- T. Ogawa. Travelling wave solutions to a perturbed Korteweg–de Vries equation. Hiroshima Math. J., 24(2):401–422, 1994.
- T. Ogawa. Periodic travelling waves and their modulation. Jpn. J. Ind. Appl. Math., 18(2):521–542, 2001. http://dx.doi.org/10.1007/BF03168589.
- Y. Tang, W. Xu, J. Shen and L. Gao. Persistence of solitary wave solutions of singularly perturbed Gardner equation. Chaos Soliton Fractals, 37(2):532–538, 2008. http://dx.doi.org/10.1016/j.chaos.2006.09.044.