The Solution Of Variable Coefficient Sine-Gordon Equation And Hirota Equation

This paper mainly study two important equations for AKNS system: the Variablecoefcient Sine-Gordon equation and constant coefcient Hirota equation, this twononlinear integrable equations play an important role in the nonlinear science.First, for the Hirota equation, the form of the determinant for solutions is given,and by making use of this determinant, the higher order rogue waves are obtained,further, we also give the analysis for the kinds of the solutions and their properties.Second, for the variable coefcient Sine-Gordon equation, we are based on thecontact with the constant coefcient Sine-Gordon equation, by making use of thetransformation between the constant coefcient Sine-Gordon equation and the vari-able coefcient Sine-Gordon equation, we change the former’s solutions into the solu-tions of variable coefcient Sine-Gordon equation, moreover, we also obtain the roguewave for the variable coefcient Sine-Gordon equation, finally, the discussion about theapplication of these solutions is given.