WIAS Preprint No. 2529, (2018)
Generalized integrable evolution equations with an infinite number of free parameters
- Akhmediev, Nail
- Ankiewicz, Adrian
- Amiranashvili, Shalva
- Bandelow, Uwe
2010 Mathematics Subject Classification
- 37K10 37K40 35Q55
2008 Physics and Astronomy Classification Scheme
- 02.30.Ik 05.45.Yv 42.65.Tg 47.35.Fg
- Nonlinear Schröder equation, Sasa--Satsuma equation, Hirota equation, hierarchy integrability
Evolution equations such as the nonliear Schrödinger equation (NLSE) can be extended to include an infinite number of free parameters. The extensions are not unique. We give two examples that contain the NLSE as the lowest-order PDE of each set. Such representations provide the advantage of modelling a larger variety of physical problems due to the presence of an infinite number of higher-order terms in this equation with an infinite number of arbitrary parameters. An example of a rogue wave solution for one of these cases is presented, demonstrating the power of the technique.
- Workshop on Nonlinear Water Waves, S. Murashige, ed., vol. 2109 of RIMS Kôkyûroku Bessatsu, RIMS, Kyoto, 2019, pp. 33--46.