In this work, we study the integrable sinh-Gordon (ShG) and the modified KdV-sinh-Gordon (MKdV-ShG) equations. We show that these two equations pass the Painlev´e test to confirm its integrabilities. We establish new complex forms of the simplified Hirota’s method, to formally derive multiple complex soliton solutions for each equation. Our results show that the complex simplified Hirota’s method explicitly constructs new multiple complex soliton solutions in addition to the multiple real soliton solutions that each equation generates.
Digital Object Identifier (DOI)
"Multiple Complex Soliton Solutions for the Integrable Sinh-Gordon and the Modified KdV-Sinh-Gordon Equation,"
Applied Mathematics & Information Sciences: Vol. 12
, Article 1.
Available at: https://dc.naturalspublishing.com/amis/vol12/iss5/1