Abundant soliton solutions for the Kundu-Eckhaus equation via tan(ϕ(ξ))-expansion method

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• 作者：Jalil Manafian ; ^{j_manafianheris@tabrizu.ac.ir" class="auth_mail" title="E-mail the corresponding author} ; Mehrdad Lakestani ^{lakestani@tabrizu.ac.ir" class="auth_mail" title="E-mail the corresponding author}
• 关键词：02.60.Lj ; 02.70.Wz ; 02.90.+p ; 04.30.Nk
• 刊名：Optik - International Journal for Light and Electron Optics
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：127
• 期：14
• 页码：5543-5551
• 全文大小：1303 K

文摘

In this paper, the improved class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0030402616302091&_mathId=si1.gif&_user=111111111&_pii=S0030402616302091&_rdoc=1&_issn=00304026&md5=cb4350b147c54e2921ab554ef680d7bf" title="Click to view the MathML source">tan(Φ(ξ)/2)class="mathContainer hidden">class="mathCode">$tan\left(\Phi (\xi )/2\right)$-expansion method is proposed to seek more general exact solutions of the Kundu–Eckhaus equation. Being concise and straightforward, this method is applied to the nonlinear Kundu–Eckhaus equation. The exact particular solutions containing five types hyperbolic function solution (exact soliton wave solution), trigonometric function solution (exact periodic wave solution), rational exponential solution (exact singular kink-type wave solution), logarithmic solution and rational solution (exact singular cupson wave solution). We obtained further solutions comparing this method with other methods. The results demonstrate that the new class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0030402616302091&_mathId=si1.gif&_user=111111111&_pii=S0030402616302091&_rdoc=1&_issn=00304026&md5=cb4350b147c54e2921ab554ef680d7bf" title="Click to view the MathML source">tan(Φ(ξ)/2)class="mathContainer hidden">class="mathCode">$tan\left(\Phi (\xi )/2\right)$-expansion method is more efficient than the Ansatz method applied by Baskonus et al. [16]. Recently this method developed for searching exact travelling wave solutions of nonlinear partial differential equations. Abundant exact travelling wave solutions including solitons, kink, periodic and rational solutions have been found. These solutions might play important role in engineering and physics fields.