Abstract
Abstract This work proposes the new extended rational sinh-Gordon equation expansion technique (SGEEM). The computational approach is formulated based on the well-known sinh-Gordon equation. The proposed technique generalizes the sine-Gordon/sinh-Gordon expansion methods in a rational format. The efficiency of the suggested technique is tested on the (2+1)imensional Kunduukherjeeaskar (KMN) model. Various of optical soliton solutions have been obtained using this new method. The conditions which guarantee the existence of valid solitons are given.
Highlights
Analysis of the MethodWe give the description of the novel extended rational sinh-Gordon equation expansion technique
= =i =j Gordon/sinh-Gordon expansion methods in a rational format
The authors introduced the following trial solution which was generated from the sine-Gordon equation [45, 46]: Θ(∆)
Summary
We give the description of the novel extended rational sinh-Gordon equation expansion technique. Where the superscript indicates the derivative of the function Θ with respect to ∆. The general steps of the new generalized rational sinh-Gordon equation expansion method are given as follows: Step-I: Suppose that Eq (2.6) adopts the following form of rational solution: Θ(Ω) = ∑mj=1 ∑mj=1 b j sinh(Ω) + a j cosh(Ω) c j sinh(Ω) + d j cosh(Ω). Step II: The unknown parameters involved are obtained by substituting Eq (2.9) along with Ω = sinh(Ω) and/or Ω = cosh(Ω) into Eq (2.8). This produces a polynomial in powers of hyperbolic functions. Step III: The solutions of Eq (2.6) are reached by inserting the values of the unknown parameters into the following rational solutions formed from Eqs.
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