https://orcid.org/0000-0003-2371-8886
References
- Kano K, Nakayama T. An exact solution of the wave equation ut+uux−u5x=0. J Phys Soc Jpn. 1981;50:361–362. doi: 10.1143/JPSJ.50.361
- Andrade TP, Crisófani F, Natali F. Orbital stability of periodic traveling wave solutions for the Kawahara equation. J Math Phys. 2017;58:051504. doi: 10.1063/1.4980016
- Byrd PF, Friedman MD. Handbook of elliptic integrals for engineers and scientists. 2nd ed. New York: Springer; 1971.
- Andrade TP, Pastor A. Orbital stability of periodic traveling-wave solutions for the BBM equation with fractional nonlinear term. Phys D. 2016;317:43–58. doi: 10.1016/j.physd.2015.12.002
- Albert JP. Positivity properties and stability of solitary-wave solutions of model eqautions for long waves. Comm Part Differ Equ. 1992;17:1–22. doi: 10.1080/03605309208820831
- Angulo J, Natali F. Positivity properties of the Fourier transform and the stability of periodic travelling-wave solutions. SIAM J Math Anal. 2008;40:1123–1151. doi: 10.1137/080718450
- Alves G, Natali F, Pastor A. Sufficient conditions for orbital stability of periodic traveling waves. J Differ Equ. 2019;267:879–901. doi: 10.1016/j.jde.2019.01.029
- Stuart CA. Lectures on the orbital stability of standing waves and applications to the nonlinear Schrödinger equation. Milan J Math. 2008;76:329–399. doi: 10.1007/s00032-008-0089-9
- Kwak C. Well-posedness issues on the periodic modified Kawahara equation; 2019. Available from: https://arxiv.org/abs/1902.08946.
- Cristófani F, Natali F, Pastor A. Orbital stability of periodic traveling-wave solutions for the Log-KdV equation. J Differ Equ. 2017;263:2630–2660. doi: 10.1016/j.jde.2017.04.004
- Natali F, Pastor A. The fourth-order dispersive nonlinear Schrödinger equation: orbital stability of a standing wave. SIAM J Appl Dyn Syst. 2015;14:1326–1347. doi: 10.1137/151004884
- Parkes EJ, Duffy BR, Abbot PC. The Jacobi elliptic-function method for finding periodic-wave solutions to nonlinear evolution equations. Phys Lett A. 2002;295:280–286. doi: 10.1016/S0375-9601(02)00180-9
- Kiper A. Fourier series coefficients for powers of the Jacobian elliptic functions. Math Comput. 1984;43:247–259. doi: 10.1090/S0025-5718-1984-0744934-6