Nonlinear Waves

I’ve been researching nonlinear waves since I was a college freshman in 2000.

• Papers and Mathematica packages

Nonlinear Ocean Waves

• Phys. Rev. E, vol. 86, pp. 036305 (2012). (APS) (ArXiv) See photos here. Synopsis on APS's Physics.

Dispersive Shock Waves

• Phys. Rev. E, vol. 87, pp. 022906 (2013). (APS)
• Phys. Lett. A, vol. 377, pp. 555–559 (2013). (DOI) (ArXiv)
• Phys. Rev. E, vol. 80, pp. 016603 (2009). (APS) (ArXiv)

Integrability

• Recursion operators: Int. J. Comp. Math., vol. 87(5), pp. 1094–1119 (2010). (Taylor&Francis) (ArXiV)
• Painlevé test: J. Nonlinear Math. Phys., vol. 13(1), pp. 90–110 (2006). (JNMP) (ArXiv)

Special Solutions

• DDEs: Comp. Phys. Comm., vol. 162(3), pp. 203–217 (2004). (ArXiv)
• PDEs: J. Symb. Comp., vol. 37, pp. 669–705 (2004). (ArXiv)