The first integral method to some complex nonlinear partial differential equations

Abstract

a r t i c l e i n f o MSC: 35Q55 35Q80 35G25 Keywords: First integral method New Hamiltonian amplitude equation Coupled Higgs field equation a b s t r a c tIn this paper, the first integral method is used to construct exact solutions of the Hamiltonian amplitude equation and coupled Higgs field equation. The first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones.Crown

New Exact Solutions of the New Hamiltonian Amplitude-Equation and Fokas Lenells Equation

“…[24], the solution Equation (22) in [27], the solution Equation (23) in [31], the solution Equation (53) in [32] and the solution Equation (53) in [33] in this study as the solution Equation (40). Besides, we have found the similar solution with the solution Equation (59) in [24] and the solution Equation (54) in [33] in this study as the solution Equation (42).…”

“…Many authors have tackled numerous methods to find exact solutions of the new Hamiltonian amplitude equation such as the general projective Riccati equation method [24], the sinh-Gordon expansion method [25], the extended F-expansion method [26], the first integral method [27], the G / G ′ -expansion method [28], the functional variable method [29], Lie symmetry method [30], the simplest equation method [31], He's semi-inverse variational principle method and Ansatz method [32], modified simplest equation method [33].…”

“…Firstly, we consider the following new Hamiltonian amplitude equation [22][23][24][25][26][27][28][29][30][31][32][33]:…”

“…Also, in Figures 3 and 4, we draw two and three dimensional graphics of imaginary and real values of Equation (27), which demonstrate the dynamics of solutions with convenient parametric choices. In Figures 5 and 6, we plot two and three dimensional graphics of Equation (44), which represent the dynamics of solutions with proper parametric values.…”

Soliton solutions of coupled systems by improved (Gʹ/G)-expansion method

“…(20) in Eq. (19) and according to Eqs. (8), (9), (10) and (11), we obtain the following exponential function solutions, hyperbolic function solutions and triangular function solutions of the coupled Higgs equation as follows:…”