Soliton solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics


Mirzazadeh M., EKİCİ M. , SÖNMEZOĞLU A. , Ortakaya S., Eslami M., Biswas A.

EUROPEAN PHYSICAL JOURNAL PLUS, vol.131, no.5, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 131 Issue: 5
  • Publication Date: 2016
  • Doi Number: 10.1140/epjp/i2016-16166-7
  • Title of Journal : EUROPEAN PHYSICAL JOURNAL PLUS

Abstract

This paper studies a few nonlinear evolution equations that appear with fractional temporal evolution and fractional spatial derivatives. These are Benjamin-Bona-Mahoney equation, dispersive long wave equation and Nizhnik-Novikov-Veselov equation. The extended Jacobi's elliptic function expansion method is implemented to obtain soliton and other periodic singular solutions to these equations. In the limiting case, when the modulus of ellipticity approaches zero or unity, these doubly periodic functions approach solitary waves or shock waves or periodic singular solutions emerge.