2018
DOI: 10.1007/s11082-018-1682-y
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Analytical study of exact traveling wave solutions for time-fractional nonlinear Schrödinger equations

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Cited by 18 publications
(4 citation statements)
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“…The second problem is the nonlinear fractional Phi-4 equation for which the (G /G, 1/G)-expansion method will be used. Some recent work utilizing the conformable fractional derivative in real world problems such the Burgers-KdV equation, the KdV-Zakharov-Kuznetsev equation, the unstable Schrödinger equation, and the resonant nonlinear Schrödinger equation have been studied in [28][29][30]. In addition, exact solutions to equations associated with the above two problems have been found using many methods.…”
Section: Introductionmentioning
confidence: 99%
“…The second problem is the nonlinear fractional Phi-4 equation for which the (G /G, 1/G)-expansion method will be used. Some recent work utilizing the conformable fractional derivative in real world problems such the Burgers-KdV equation, the KdV-Zakharov-Kuznetsev equation, the unstable Schrödinger equation, and the resonant nonlinear Schrödinger equation have been studied in [28][29][30]. In addition, exact solutions to equations associated with the above two problems have been found using many methods.…”
Section: Introductionmentioning
confidence: 99%
“…Fractional nonlinear evolution equations (FNLEEs), are mathematical models that describe many complicated phenomena in nature and science particularly, fiber-optic communication, transport processes, plasma physics, bio-engineering, signal processing, fluid dynamics, control theory, fractal theory, nuclear reactor kinetics, electrical circuits, and viscoelastic materials, etc [1,2]. Some noteworthy FNLLEs in the aforementioned domains are the family of Schrodinger equations [3][4][5], the Heisenberg ferromagnetic spin chain [6], Kundu-Eckhaus equation [7], the reaction-diffusion equation [8], the NPCLL equation [9], The Boussinesq equation [10], Kadomtsev-Petviashvili equation [11], The Klein-Gordon equation [12], The Zakharov-Kuznetsov (ZK) equation [13], and so on. The analytical solution of these equations piqued the interest of both theoretical and experimental researchers in the last few decades.…”
Section: Introductionmentioning
confidence: 99%
“…Based on the homogeneous balance principle of soliton theory, numerous techniques have been discovered. For instance, the Sine-Gordon expansion scheme [5], the auxiliary equation method [6], the tanh-coth method [14], the modified -expansion and modified Kudryashov methods [15], the modified -expansion function strategy [9], the Kudryashov scheme [16], the extended Kudryashov method [17], and so on. The analytical solutions derived using the methods described in the above are a sort of traveling wave solution known as a soliton solution.…”
Section: Introductionmentioning
confidence: 99%
“…The authors in [17] introduced a useful conformable derivative; in addition, a non-conformable derivative is introduced in [18]. These derivatives are interesting from a theoretical viewpoint and useful in many applications [19][20][21].…”
Section: Introductionmentioning
confidence: 99%